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

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.
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?
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sonorous9n
$95 and loses$2 each day
ler $x=$ number of days
$y=$ value after x 30 day period
$y=95-2x$ (1)
$y=75-1.5x$ (2)
When gift card will have equal value 1=2
$95-2x=75-1.5x\to$ equation to find 30-day period until gift card has equal value
$95-75=\left(2-1.5\right)x$
$0.5x=20$
$x=40$
a) 30 day period value of gift card will be equal.
after $40×30=1200$ days
b) Value of card when equal
1) $y=95-2x$
$y=95-2×40$
$y=15$
for (2)
$y=75-1.5x$
$y=75-1.5×40$
$y=15$
Answer: $15 each card will have$15 as equal value.

Philip Williams

Gift Card 1 $\left(C=GC1\right)$ has a value of
Mathematically, lets set T for a time increment of 30 days. .
So we can state the value of GC1, in increments of 30 days, as .
And so,
We want to know the value of T when the cards are equal in value.
So for what value of T does $GC1=GC2$?
$95-T\cdot 2=75-T\cdot 1.5$, 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: $\mathrm{}95-\left(40\cdot \mathrm{}2\right)=\mathrm{}15$
Card 2: $\mathrm{}75-\left(40\cdot 1.5\right)=\mathrm{}15$.

alenahelenash
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. $95-2\left(\text{months}\right)=75-1.5\left(\text{months}\right)$If we move dollars to the left and months to the right, we'll get: $20=.5\left(x\right)$ 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.)