Brett is joining a new gym. He can join Power Plus or Heavy Hulk. At Power Plus, it will cost $34.14 per month, plus a sign-up fee of $22.00. At Heavy Hulk, it will cost $34.39, plus a sign-up fee of $34.50. Right now, Heavy Hulk is cutting their sign-up fee in half for new members. If Brett signs up at a gym today, after how many months will the cost of the memberships be the same?

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absor201 absor201 · Answer 1 · 2020-01-19T08:37:12+01:00

After 19 months, the cost will be same for both memberships.

Step-by-step explanation:

Given,

Sign up fee at Power Plus = $22.00

Per month fee = $34.14

Let,

x be the number of months.

P(x) = 34.14x + 22

Sign up fee at Heavy Hulk = $34.50

As they have cut the cost into half.

Sign up fee = [tex]\frac{34.50}{2}=\$17.25[/tex]

Per month fee = $34.39

H(x) = 34.39 + 17.25

For same cost ;

P(x) = H(x)

[tex]34.14x+22=34.39x+17.25\\22-17.25=34.39x-34.14x\\4.75= 0.25x\\0.25x=4.75\\[/tex]

Dividing both sides by 0.25

[tex]\frac{0.25x}{0.25x}=\frac{4.75}{0.25}\\x=19[/tex]

After 19 months, the cost will be same for both memberships.

Keywords: function, division

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