Question

Tavon has a $50 gift card that loses $2 for each 30-day period it is not used. He also has a $40 gift card that loses $1.50 for each 30-day period that it is not used. Write and solve an equation for the number of 30-day periods until the value of the gift cards will be equal.

Answer 1

20

Explanation:

The first equation is 50 - 2x (because you start with $50 and subtract 2 for each 30 day period)

The second equation is 40-1.5x

Set them equal to each other: 50 - 2x = 40 - 1.5x

Solve for x:

50 - 2x = 40 - 1.5 x

+2x +2x

-----------------------

50 = 40 + 0.5 x

-40 -40

-------------------

10 = 0.5 x

20 = x

So there will be 20 30-day periods until the cards will be equal in value.

Check: After 20 periods, 50 - 2(20) = $10 left

40 - 1.5(20) = also $10 left