For the first gift card, the value after x periods will be $105 - $2.50x.
For the second gift card, the value after x periods will be $85 - $2x.
We want to find the number of 30-day periods until the values of the gift cards will be equal, so we can set up the equation:
105 - 2.50x = 85 - 2x
Now we can solve for x:
105 - 2.50x + 2x = 85
105 - 85 = 2.50x - 2x
20 = 0.50x
x = 20/0.50
x = 40
Therefore, it will take 40 30-day periods until the values of the gift cards will be equal.
To find the value of each card at that time, we substitute x = 40 into either equation.
For the first gift card: 105 - 2.50(40) = 105 - 100 = $5
For the second gift card: 85 - 2(40) = 85 - 80 = $5
Therefore, the value of each gift card when they have equal value will be $5.
Tavon has a gift card for $105 that loses $2.50 for each 30-day period it is not used. He has another gift card for $85 that loses $2 for each 30-day period it is not used. Write and solve an equation for the number of 30-day periods until the value of the gift cards will be equal. What will the value of each card be when they have equal value? W . If x is the number of 30-day periods. then the equation can be used to find the number of 30-day periods until the values of the gift cards will be equal. Type an equation. Use integers or decimals for any numbers in the equation.)
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