Tavon has a gift card for $165 that loses $4 for each 30-day period it is not used. He has another gift card for $145 that loses $3.50 for each 30-day period it is not used. Write an equation for the number of 30-day periods until the value of the gift cards will be equal. Let x represent the number of 30-day periods.

Equation 1 = Equation 2

165 - 4x = 145 - 3.50x

Step-by-step explanation:

Let x represent the number of 30-day periods.

Tavon has a gift card for $165 that loses $4 for each 30-day period it is not used.

Therefore the equation =

$165 -$4 × x

= 165 - 4x Equation 1

He has another gift card for $145 that loses $3.50 for each 30-day period it is not used.

$145 -$3.50 × x

= 145 - 3.50x Equation 2

Hence, an equation for the number of 30-day periods until the value of the gift cards will be equal is obtained by equating Equation 1 and Equation 2 together

So, we have

Equation 1 = Equation 2

165 - 4x = 145 - 3.50x

We simplify further:

165 - 145 = -3.50 + 4.0x

20 = 0.5x

x = 20/0.5

x = 40

Therefore, number of each 30-day periods until the value of the gift cards will be equal is 40

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