Tavon has a gift card for $70 that loses $3 for each 30-day period it is not used. he has another gift card for $ 60 that loses $ 2.50 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? what will be the equation?

a. Equation:  

 The value of gift cards will be equal after 20 30-day-periods.

b. The value of each gift card when they have equal values will be $10.

Equation:

Step-by-step explanation:

Let be "x" the number of 30-day periods.

a. We know that Tavon has a gift card for $70 and it loses $3 for each 30-day period it is not used. This can be expressed as:

The other gift card for $ 60 loses $ 2.50 for each 30-day period it is not used. Then:

When the value of the gift cards are equal:

Solve for "x":

Therefore, the value of the gift cards will be equal after 20 30-day-periods.

b. Let be "y" the value of each card (in dollars) when they have equal value. Choose one the expressions shown above. Let's pick the first expression . Then:

Substitute into the equation, then:

Evaluate it in order to find what will be the value of each card when they have equal value:

A.

Solution:

B. The value of each card after twenty 30-day periods will be $10

Step-by-step explanation:

Let x be the number of 30-day periods.

First gift card:

Amount = $70

Lose for one 30-day period = $3

Lose for x 30-day periods = $3x

Left = $(70-3x)

Second gift card:

Amount = $60

Lose for one 30-day period = $2.50

Lose for x 30-day periods = $2.50x

Left = $(60-2.50x)

If the value of the gift cards are equal, then

Solve this equation. First, separate variables and numbers into different sides:

Multiply by 10:

If x = 20, then