Tavon has a gift card for $95 that loses $2 for each 30-day period it is not used. He has another gift card for $75 that loses $1.50 for each 30-day period it is not used.

Question

When the gift cards have equal value the value of each will be?

Answer 1

Hi, Annaly,

Gift Card 1 (C=GC1) has a value of $95 - Time*(-$2/30 days)

Mathematically, lets set T for a time increment of 30 days. 1 T = 30 days.

So we can state the value of GC1, in increments of 30 days, as GC1 = 95 - T*($2/30days).

And so, GC2 = 75 - T*($1.5/30days)

We want to know the value of T when the cards are equal in value.

So for what value of T does GC1 = GC2?

95-T*2 = 75 - T*1.5, where T is in increments of 30 days.

Rearranging, 20 = 0.5T

T = 40

After 40 30-day periods (1200 days), both cards should have equal value (assuming you don't use them in the meantime). Let's check it:

Card 1 after 40 periods: $95 - (40*$2) = $15

Card 2 " " : $75 - (40*1.5) = $15.

It works! Go spend them now (or have Travon send them to me).

Answer 2

The first part to solving this equation is to put one fact against another and set them to be equal each other.

Gift card one starts at $95 and loses $2 per month, while gift card two starts at $75 and loses $1.50 per month.

$95 - $2(months) = $75 - $1.5(months)

If we move dollars to the left and months to the right, we'll get:

$20 = $.5(x)

Dividing both sides by the coefficient of x ($.5) will yield the number of months until both gift cards are of equal value.

Substituting that number of months for x in our original equation will yield the dollar amount.

(After 40 months, each of the cards will be $15.)

Answer 3

p represents the number of periods

95 - 2p = 7.50 - 1.5p

Can you solve for p and answer?