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?

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?

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?

You can still ask an expert for help

sonorous9n

Answered 2022-01-17
Author has **34** answers

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

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

$0.5x=20$

$x=40$

a) 30 day period value of gift card will be equal.

after$40\times 30=1200$ days

Answer: 40

b) Value of card when equal

1)$y=95-2x$

$y=95-2\times 40$

$y=15$

for (2)

$y=75-1.5x$

$y=75-1.5\times 40$

$y=15$

Answer: $15 each card will have $15 as equal value.

$95 and loses $2 each day

ler

When gift card will have equal value 1=2

a) 30 day period value of gift card will be equal.

after

Answer: 40

b) Value of card when equal

1)

for (2)

Answer: $15 each card will have $15 as equal value.

Philip Williams

Answered 2022-01-18
Author has **39** answers

Gift Card 1

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

Rearranging,

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:

Card 2:

alenahelenash

Answered 2022-01-24
Author has **343** answers

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. $\$95-\$2(\text{months})=\$75-\$1.5(\text{months})$ 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.)

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