Question

Tavon has a gift card for $55 that loses $2 for each 30-day period it is not used. He has another gift card for $45 that loses $1.50 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 1

a. 20

b. $15

Explanation:

We can say that
`x` represent the 30-day period, then we can write the next equation:

`55-2x=45-1.5x`

Finding the
`x`, we find the number of 30-day periods until the value of the cards will be equal, then:

`55-2x=45-1.5x\\55-45=-1.5x+2x\\10=0.5x\\(10)/(0.5)=x\\\\20=x`

Then is needed a 20 30-day periods to have the cards with equal value.

Now to know the walue of each card we have:

`55-2x\\55-2(20)\\55-40=15`

Then each card will have a value of $15