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Tavon has a gift card for $55 that loses $2 for each 30-day period it is not used. He has another gift card for $45 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?

Respuesta :

2134jenny

Answer:

a. 20

b. $15

Step-by-step explanation:

We can say that [tex]x[/tex] represent the 30-day period, then we can write the next equation:

[tex]55-2x=45-1.5x[/tex]

Finding the [tex]x[/tex], we find the number of 30-day periods until the value of the cards will be equal, then:

[tex]55-2x=45-1.5x\\55-45=-1.5x+2x\\10=0.5x\\\dfrac{10}{0.5}=x\\\\20=x[/tex]

Then is needed a 20 30-day periods to have the cards with equal value.

Now to know the walue of each card we have:

[tex]55-2x\\55-2(20)\\55-40=15[/tex]

Then each card will have a value of $15

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