Tavon has a gift card for $ 90 that loses $ 4 for each 30-day period it is not used. He has another gift card for $ 80 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?

Answer: it will take twenty 30-day periods until the value of the gift cards will be equal.

The value of each card be when they have equal value is $10

Step-by-step explanation:

Let x represent the number of 30-day periods until the value of the gift cards will be equal.

Tavon has a gift card for $90 that loses $4 for each 30-day period it is not used. This means that x 30-day periods, the amount left would be

90 - 4x

He has another gift card for $ 80 that loses $ 3.50 for each 30-day period it is not used. This means that x 30-day periods, the amount left would be

80 - 3.5x

For the amounts left in each card to be the same, the number of periods would be

90 - 4x = 80 - 3.5x

90 - 80 = - 3.5x + 4x

10 = 0.5x

x = 10/0.5

x = 20

The value of each card be when they have equal value is

90 - 4 * 20 = 90 - 80

= $10

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