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

Answer:

A) 40

B) $ 15

Step-by-step 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

$x = \frac{20}{0.5}$

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