Question

Tavon has a gift card for $ 155 that loses $ 3.50 for each​ 30-day period it is not used. He has another gift card for $ 135 that loses $ 3 for each​ 30-day period it is not used.

a. Write and solve an equation for the number of​ 30-day periods until the value of the gift cards will be equal.
b. What will the value of each card be when they have equal​ value?

Answer 1

A) 40

B) $ 15

Explanation:

A)An equation for the number of​ 30-day periods until the value of the gift cards will be equal

Let x be the number of time periods for which the gift card is not used, then

For the gift card $ 155 if it is not used for x periods, then the amount that will be lost is

155 - 3.50 x---------------------(1)

For the gift card $ 135 if it is not used for x periods, then the amount that will be lost is

135 - 3x---------------------- (2)

Now when both the amount lost is equal

`155 - 3.50x = 135 - 3x`

solving the equation, we get

`155 -135 = -3x + 3.50x`

20 = 0.5x

`x = (20)/(0.5)`

x = 40

Thus the value of gift cards will be equal for 40 ,30 day periods.

B)The value of each card be when they have equal​ value

The two cards will have equal value after 40 30 day periods, this denotes that at this time, the value of each card will be equal.

Then

`155 - 3.50x = 135 - 3x`

substituting x = 40, we get

`155 - 3.50(40)= 135 - 3(40)`

`155 - 140= 135 - 120`

`15 =15`

when they have equal​ value, the value of each card will be $15