Video games math

Question

A video game store allows customers to rent games for 4.75 each customers can also buy a membership for $54 annually and video games would only cost $2.50 each write and solve an equation to find the number of video games a customers would have to rent in a year in order for the two options to be equal

Answer 1

A video game store allows customers to rent games for 4.75 each customers can also buy a membership for $54 annually and video games would only cost $2.50 each write and solve an equation to find the number of video games a customers would have to rent in a year in order for the two options to be equal

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Word problems can be tricky. The key is too....

1. Read the problem once forward.
2. Repeat step one. Read it Again
3. Try to find the singular question the problem is asking for.....

All WORD problems have some sort of embedded equation (something is equal to something else).

There is always something UNKNOWN being investigated.

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Let X be the number of video games purchased

and let T1 and T2 be each options TOTAL cost.

.....now we translate the word problems to math problems given we are using X and T as an unknown variables.....so....

OPTION #1

54 + 2.50 * X = T1

OPTION #2

4.75 * X = T2

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Now you are looking for the options where T1=T2 or T........

54 + 2.5 (X) = T

4.75(X ) = T

.....you now have a common problem in Algebra....2 equations and 2 unknowns.....

....from the problem description.....when does option 1 equal option 2....or....

54 + 2.5X = 4.75 X

-2.5X -2.5X......................subtract 2.5X from both sides

54 = 2.25 X

/2.25 /2.25.............................divide both sides of the equation by 2.25 to solve for X

54/2.25 = X = 24....or X= 24

----now CHECK...CHECK....CHECK this value in each option----

Option #1

54 + 2.5 (X) = T1.......54 + 2.5 (24) = 54 + 60 = 114

Option #2

4.75 * X = T2............4.75 (24) = 114

.....so the value of 24 CHECKS out......Right?

....REMEMBER....the question asks....

find the number of video games a customers would have to rent in a year in order for the two options to be equal

THAT NUMBER X = 24 .......Right?

Answer 2

Hello, Momo,

Make an equation in which the rental-only option is set equal to the membership/rent option. Let X = number of rented games. The left side is the cost of games rented over the course of a year, and the right side is for a yearly membership plus the same number of games for a year, but now costing 2.50 each, not 4.75.

Solve the resulting equation for X and you'll see that the costs are equal if you rent 24 games/year.

Bob