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Tavon has a gift card for 125 that loses $3 for each​ 30-day period it is not used. He has another gift card for 105 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?

Respuesta :

adioabiola

The value of each gift card be when they have equal value is $5 respectively.

Equation

Let

  • Number of 30-day period it is not used = x
  • Value of the gift card = y

Gift card 1:

y = 125 - 3x

Gift card 2:

y = 105 - 2.50x

  • Equate the gift card values

125 - 3x = 105 - 2.50x

125 - 105 = -2.50x + 3x

20 = 0.50x

x = 20 / 0.50

x = 40

So,

The value of each card be when they have equal value

Gift card 1:

y = 125 - 3x

y = 125 - 3(40)

= 125 - 120

y = $5

Gift card 2:

y = 105 - 2.50x

= 105 - 2.50(40)

= 105 - 100

y = $5

Therefore, the value of each gift card be when they have equal value is $5 respectively.

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