 # Tavon has a gift card for $95 that loses$2 for each 30-day period it is not used. He has another gi Sallie Banks 2022-01-16 Answered
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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For first gift card
$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.

We have step-by-step solutions for your answer! 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: $\mathrm{}75-\left(40\cdot 1.5\right)=\mathrm{}15$.

We have step-by-step solutions for your answer! 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.)

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