Nina wants to download games for her video game console. Older games cost 150 points and new releases cost 600 points. Nina has 6000 points to use. The equation 150a+600b=6000, where a is the number of older games and b is the number of new releases, models the situation. How many older games can she download if she downloads one new game? four new games?

Answers

Answer 1

Considering the definition of an equation and the way to solve it, Nina can download 36 older games and 24 older games if she downloads one and four new games respectively.

Definition of equation

An equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns, appear in addition to certain known data.

The solution of a equation means determining the value that satisfies it and the equality is true. To solve an equation, keep in mind:

When a value that is adding, when passing to the other member of the equation, it will subtract.If a value you are subtracting goes to the other side of the equation by adding.When a value you are dividing goes to another side of the equation, it will multiply whatever is on the other side.If a value is multiplying it passes to the other side of the equation, it will pass by dividing everything on the other side.

This case

In this case, Nina wants to download games for her video game console.  Older games cost 150 points and new releases cost 600 points. Nina has 6000 points to use.

The equation 150a+600b=6000, where a is the number of older games and b is the number of new releases models the situation.

If Nina downloads one new game, that means that the value of the variable "b" is 1. Substituting in the equation that models the previously mentioned situation, and solving, you obtain:

150a+600×1=6000

150a + 600=6000

150a= 6000 - 600

150a= 5400

a= 5400÷150

a= 36

If Nina downloads four new game, that means that the value of the variable "b" is 4. Substituting in the equation that models the previously mentioned situation, and solving, you obtain:

150a+600×4=6000

150a + 2400=6000

150a= 6000 - 2400

150a= 3600

a= 3600÷150

a= 24

Finally, Nina can download 36 older games and 24 older games if she downloads one and four new games respectively.

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Related Questions

The total cost of a jacket and a pair of pants was $52.37. If the price of the jacket was $4.87 less than the pair of pants, what was the price of the jacket? Express your answer as a simplified fraction or a decimal rounded to two places.

Answers

The price of the jacket is $23.75

Let m be the price of a jacket and n be the price of pair of pants.

The total cost of a jacket and a pair of pants was $52.37

So, we get an equation,

m + n = 52.37              ................(1)

Also, the price of the jacket was $4.87 less than the pair of pants

So, we get an equation,

m = n - 4.87               .............(2)

Substitute above value of m in equation (1)

⇒ (n - 4.87) + n = 52.37

⇒ 2n - 4.87 = 52.37

⇒ 2n = 52.37 + 4.87

⇒ 2n = 57.24

⇒ n = 28.62

This means, the cost of a pair of pants is $28.62

Substitute above value of n in equation (2)

⇒ m = n - 4.87

⇒ m = 28.62 - 4.87

⇒ m = 23.75

This means, the cost of a jacket is $23.75

Therefore, the price of the jacket is $23.75

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A more
at a lower cost
business generally achieves greater profits

Answers

Answer:

What do you need help with?

Step-by-step explanation:

nth term of -9, -5, -1, 3, 7

Answers

The nth term of the given sequence is 4n - 1.

What do we mean by the nth term?The nth term is a formula that allows us to locate any term in a series. The 'n' represents the term number. By substituting different values for the term number, we can create a sequence using the nth term ( n ).

So,

-9 + 4 = -5-5 + 4 = -1-1 + 4 = 33 + 4 = 7As, (4 × 2) - 1 = 7Then, the nth term is 4n - 1

Therefore, the nth term of the given sequence is 4n - 1.

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Write three different expressions that equivalent to 8 to the power 2 x 4 to the power of 2

Answers

Answer:

One could be: 8*8 times 4*4

Another could be: 8 to the second power times 4 to the second power

A third way to write this could also be: 8*4*8*4

Step-by-step explanation:

Hope its helpful

Find the probability that there are no T when a fair coin is flipped three times.

Answers

The probability that no Tails is achieved on flipping a fair coin for three consecutive times is [tex](\frac{1}{8})[/tex].

As per the question statement, we are to flip or toss a fair coin thrice consecutively.

We are required to calculate the probability that no Tails is achieved during the above mentioned event.

To solve this question, first let us calculate all the possible outcomes of flipping a fair coin thrice consecutively. [We will denote a Heads outcome as "H" and a Tails outcome as "T"]

The total number of outcomes can be given by the formula [tex](2^{n})[/tex], where "n" is the number of times, the coin is tossed.

Here, (n = 3), therefore, total number of outcomes in our case [tex]=(2^{3})=8[/tex].

These 8 outcomes can be listed as [tex][{(H, H, H), (H, H, T), (H, T, H), (H, T, T), (T, H, H), (T, H, T), (T, T, H), (T, T, T)}][/tex]

And among the above listed 8, our favorable outcome is (H, H, H), i.e., 1 favorable outcome of 8.

Hence, probability that no Tails is achieved on flipping a fair coin thrice consecutively = [tex]\frac{1}{8}[/tex].

Probability: In Mathematics, probability is the chance to of the occurrence of a specific event among the occurrence of all possible events, and is measured by the ratio of the favorable cases to the whole number of cases possible.

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What is the volume, in cubic inches, of a cylinder with a radius of 4 inches
and a height of 12 inches? (Use 3.14 for pi.)

Answers

Answer:

602.88 cubic inches

Step-by-step explanation:

Volume of cylinder = pi ×r^2×height

=3.14×4^2×12

=3.14×16×12

=602.88

Solve for x.
-4x+60 < 72
OR 14z +11 <-31

Answers

The value of x is 3 and  -3 respectively.

How to solve the inequality

Given that;

4x+60 < 72     (1)14x +11 <-31      (2)

From equation (1)

4x+60 < 72  

First, collect like terms

4x < 72 - 60

subtract like terms

4x < 12

Make 'x' the subject

x < 12/ 4

x < 3

For equation (2)

14x +11 <-31

collect like terms

14x < -31 - 11

14x < -42

Make 'x' the subject

x < -42/ 14

x < -3

Thus. the value of x is 3 and  -3 respectively.

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How do you solve this Зп – 1

Answers

Step-by-step explanation:

3n just means 3 × n

To actually solve the equation, the value of n would have to be given.

In some equations, you would have to solve for n and then answer the equation, but that's not possible with this one.

A music club has 24 members. Each member pays monthly dues of $8.75. On the first day of the month, 16 members paid their dues. The remaining members paid their dues on the second day of the month. How much money was collected in dues on the second day of the month?

Answers

Answer:

$70

Step-by-step explanation:

$70 was collected on the second day of the month.

9x7/9-6+13 order of Operations

Answers

((9×7)÷9−6)+13

(63÷9−6)+13

(7−6)+13

1+13

14

Answer:

9 X 7 / 9 - 6 + 13

we can cut 9

=7-6 + 13

=1+13

=14

rotation 90° counterclockwise about the origin​

Answers

(x,y) -> (-y, x) the second point is the location of the pre image if you shift the polygon on the cartesian coordinate plane

Ms. Francis is planning a birthday party for her daughter. There will be 22 children at the party, and in order to seat them all she needs to rent square card tables. Only 1 child can sit at each side of a card table.

Ms. Francis wants to arrange the tables in a rectangular shape so they look like one large table. The room is large enough that

the rectangle can be made with more than one row of tables.

Part A: How many different arrangements can Ms. Francis make to seat all 22 children?

Part B: What is the smallest number of tables that Ms. Francis needs to rent?

DIRECTIONS: To solve the problem, apply the steps of the Mathematical Problem-Solving Routine.

Understand

1. Try to visualize the situation. Consider drawing a diagram

2. State the problem in your own words.

3. What is the important information in the problem?

Plan

4. What strategy will you use to solve the problem? Why?​

Answers

There are 5 possible arrangements to make seat all 22 children.

The smallest number of tables Ms. Francis is 10 tables.

Total number of children at the party = 22

When we picturize the scenario, each child need to get a side of the table.

So at least 22 sides should be there after arranging it into rectangles. Also the square card tables are arranged side to side to get rectangle rows.

It is also said that there can be multiple rows. So combining all these points, we can consider a row of 10 tables. Then the the squares on the ends contribute a total of 6 sides and the remaining 16 seats can be arranged by 8 square tables in between the end square tables. So a total of 10 square table is required to make a rectangle in one row.

For making 22 seats in 2 rows, the 4 square tables on the ends contribute 8 seats. For the remaining 12 seats add 7 square tables in each row, that is a total of 14 square tables. That is, for 2 rows, the square tables required is 14 + 4 = 18.

Similarly, for 3 rows, a total of 24 square tables are required.

For 4 rows, a total of 28 tables and for 5 rows, a total of 30 tables are needed.

We cannot make a 6 row because it will be same as a 5 row.

So 5 different arrangements can be made to seat all 22 children.

They are:

1 row → 1 x 10 = 10 tables

2 rows → 2 x 9 = 18 tables

3 rows → 3 x 8 = 24 tables

4 rows → 4 x 7 = 28 tables

5 rows → 5 x 6 = 30 tables

The smallest number of tables that Ms. Francis needs to rent is, therefore, 10 tables.

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Show that [16 ^1/4] ^3 and (16^3)^1/4 are equivalent

Answers

i believe they are not

7,5+9287= x + 7?????​

Answers

Answer:

X = 9287.5

Step-by-step explanation:

Solving steps

7.5+ 9287=x+7

Calculate

9294.5=x+7

Move the terms

-x=7-9294.5

Calculate

-x=-9287.5

Change the signs

Solution

X = 9287.5

Please help me, I'll give brainliest.
In below Diagram,​

Answers

The length of BE is 15 cm.

It is given that length of FA is 40 cm and CD is 24 cm.Use trigonometry or similar triangles.In ΔDAC,Tan(∠DAC) = DC/ACIn ΔEAB,Tan(∠EAB) = BE/AB∠DAC = ∠EABDC/AC = BE/AB(DC)(AB) = (BE)(AC)This is equation (1).In ΔDAC,Tan(∠FCA) = FA/ACIn ΔDAC,Tan(∠ECB) = BE/BC∠FCA = ∠ECBFA/AC = BE/BC(FA)(BC) = (BE)(AC)This is equation (2).From equations (1) and (2),(DC)(AB) = (FA)(BC)24(AB) = 40(BC)AB = BC(40/24)AB = BC(5/3)In equation (2), AC can be written as the sum of AB and BC.(FA)(BC) = (BE)(AB + BC)Use the known values.40(BC) = (BE)[(5/3)BC + BC]40(BC) = (BE)[(8/3)BC]40 = BE(8/3)BE = (40/8)*3BE = 5*3BE = 15cm

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PLEASE HELP!!! I WILL GIVE BRAINLYEST!!

The dimensions of a room are given as 3.5 meters by 7.6 meters, to the nearest 10 cm. What area of carpet should be purchased to make sure it covers all the room?

Answers

Answer: Our carpet calculator will help you determine your approximate floor area in square metres. Simply measure the length and width of each room to the nearest 10cm, i.e. 5.4m x 3.7m, then enter your totals into the calculator and hit the 'calculate' button at the bottom.  

For awkwardly shaped rooms (such as an L shape) divide the room into blocks, measure them separately and add them in as individual rooms.

Step-by-step explanation:

Identify the Property of Operation that is being used.

3(a – 2) = 3a – 6

Question 1 options:

Distributive Property


Commutative Property


Identity Property


Associative Property
-------------------------------
(5 x 4) x 2 = 5 x (4 x 2)

Question 2 options:

Commutative Property


Distributive Property


Associative Property


Identity Property

-------------------------------
Simplify the expression.

9y + 6 – 7y - 3

Question 3 options:

-2y - 3


2y + 3


2y + 9


-2y + 9

-------------------------------

9y + 6 – 7y - 3

Question 3 options:

-2y - 3


2y + 3


2y + 9


-2y + 9

-------------------------------
a + b + 2a + 2b + 5 − b

Question 5 options:

3a + 2b + 5


3a + 4b + 5


2a + 4b + 5


2a + 2b + 5

Answers

Answer:

3×a-3×2=3a-6

3a-6=3a-6 proved

3.
The Moy family budgeted $32,650 to remodel their kitchen. They spent
$43,987. How much more or less is the amount spent than the amount
budgeted?
A $11,337 more

B $11,337 less

C $17,887 more

D $17,887 less

Answers

Answer:

A

Step-by-step explanation:

43987-32650= 11337

And it’s more

Austin rented a truck for one day. There was a base fee of $17.99, and there was an additional charge of 73 cents for each mile driven. Austin had to pay $120.92 when he returned the truck. For how many miles did he drive the truck?

Answers

The miles for which  Austin drove the truck  is 141 miles

It is given that Austin rents a truck for one day

The daily rental base fee of the truck is $17.99

It is also given that additional charge of 73 cents per mile is charged.

It is also to be noted that 1$ =100 cents

Therefore, 73 cents in the form of dollar is 0.73$

Now it is given that total bill that is paid is $120.92

Now the total number of miles travelled by Austin is total bill minus the base fee and 73 cents multiplied by miles

Let the miles travelled by Austin be 'x'

Therefore, Miles travelled by Austin = 120.92$-17.99$

                                     0.73 x =(120.92 -17.99)  $                      

                                     x= 102.93 / 0.73

                                     x=141

Hence, the miles for which Austin drove the truck is 141 miles

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-7=
n-10
3
2 step eq

Answers

3(n-10)=-7

Solve the equation in 2 step equation.

n=18.5

Given that 3(n-10)=7

step1: multiplication

Adding a number to itself as many times as the value of the other number is equivalent to multiplying two numbers by their sum.

3n-30=7

step2: adding 30 on both sides of the equation.

When objects are collected together, addition, a mathematical operation, describes how many total items there are in the collection.

2n-30+30=7+30

2n=37

step3: divide the equation by 2.

Basically, dividing is the act of dividing anything into equal sections or groups.

[tex]\frac{2n}{2} =\frac{37}{2}\\ n=\frac{37}{2} or 18.5[/tex]

Therefore, n=18.5

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Estimating percents 19% of 72

Pleas explain how because I don’t understand this

Answers

Answer:

13.68

Step-by-step explanation:

72 * 0.19 = 13.68

19% can be converted to 19/100 or .19 to change out of a percentage. .19 is the multiplied by 72 to find 19% of 72.

For example

a fourth of something is the same as 25%.

if you want to find 1/4 of 8 you would multiply 8 by 1/4.

It is a similar concept with percentages.

Consider a data set with at least three data values suppose the highest value is increased by 10 and the lowest is decreased by five

Answers

plss give your self a answer

What unit would I use in this equation for science

Answers

Answer:

I think Dessicant

Step-by-step explanation:

i hope it helped you if I'm right :D

f(x) = x² - 6x-7
g(x) = x + 1

Answers

Answer:

(-1, 0) and (8, 9)

Step-by-step explanation:

x² - 6x-7 = x + 1

x² - 7x - 8 = 0

(x - 8)(x + 1) = 0

x = -1, 8.

When x = - 1, y = 0

and x = 8, y = 9

is b a scale copy of a yes or no explain your reasoning

Answers

Figure B is not a scale copy of figure A. The answer is NO. The corresponding lengths of both figures have different ratios.

How to Determine a Scale Copy of a Figure?

If a figure is the scale copy of another figure, the corresponding side lengths of both figures would be proportional to each other, which means their ratios would be the same.

From the figure given, the ratios of their side lengths are:

18/9 = 2

12/12 = 1

30/15 = 2

This shows that their ratios are not the same.

Therefore, we can conclude that figure B is not a scale copy of figure A. The answer is NO. The corresponding lengths of both figures have different ratios.

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Elroy's Balloon Emporium sells boxes of balloons. There are 500 balloons in a box. In January, they sell 3 boxes.In February they sell 6 boxes .If they started with 10 boxes, how many balloons do they have left to sell?

Answers

Answer:

500

Step-by-step explanation:

3+6=9
10-9=1

They sell 9 out of the 10 boxes. if each box has 500 balloons, then they have 500 left

Answer: 500 balloons

Step-by-step explanation: if you do 500 x 10 you get 5000 and then you do 3 x 500 + 6 x 500 then you get 4500 then subtract that from 5000

NEED ANSWER PLS HURRY !!

Answers

Answer:it's the second option

Step-by-step explanation:

-x is already -1 so why would factoring it make it -1 again

Find an expression which represents the difference when (- x - 3y) is subtracted
from (8a - 9y) in simplest terms.

Answers

Answer:

hello

Step-by-step explanation:

hi

MSA

my milkshake brings all the boys to the yard yeah right its better than yours yeah right its better than yours

PLEASE HELP ITS DUE TODAY Pleasee

Answers

[tex]scale \: from \: b \: to \: a = \frac{3}{2} \\ x = \frac{2}{3} \times 10.5 = 7[/tex]

I will mark brainliest, answer choices are:

Quadrant I
Quadrant 2
Quadrant 3
Quadrant 4
A"(0,2)
A"(1,-2)

Answers

Answer:

Quadrant 1

Step-by-step explanation:

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