Tavon has a $50 gift card that loses $2 for each 30-day period it is not used. He has a $40 card that loses $1.50 for each 30-day period it is not used.

Question

Write and solve an equation for the number of 30-day periods until the value of the gift cards will be equal

Answer 1

Let  = a 30 day period

 

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

 

Answer 2

Let p = number of 30 day periods

 

50 - 2p = 40 - 1.5p

add 1.5p to both sides

50 - 0.5p = 40

subtract 50 fom both sides

-0.5p = -10

divideboth sides by -0.5

p = 20