Question

Tavon has a gift card for $175 that loses $4 for each 30-day period it is not used. He has another gift card for $155 that loses $3.50 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? a. If x is the number of 30-day periods, then the equation can be used to find the number of 30-day periods until the values of the gift cards will be equal. (Type an equation. Use integers or decimals for any numbers in the equation.)​

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

solving the equation, we get

20 = 0.5x

x = 40Thus 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 substituting x = 40, we get when they have equal​ value, the value of each card will be $15