Question

Really don’t understand help. With picture

Answer 1

So, we can start off by just listing the facts.

The Initial fee for Jim's Gym has an initial fee of $300, and Sally's Salon has an initial fee of $250. Every visit to Jim's Gym costs $3, and Sally's Salon costs $5.

The question is using the variable x, in which x represents the number of visits that person has made.

So the equation for Jim's Gym is 300 + 3x (since, like we've established earlier, it costs $3 per visit.

The equation for Sally's Salon is 250 + 5x (since it costs $5 per visit)

Since we're trying to equalize costs, make the entire equation

300 + 3x = 250 + 5x

Subtract both sides by 250

50 + 3x = 5x

Subtract both sides by 3x

50 = 2x

Divide both sides by 2

x = 25

Option D is the answer.

Answer 2

`\bf \textit{Jim's Gym}\\\\ \begin{array}{cccll} initial~fee&visits&cost\\ \cline{1-3} 300&1&300+3(1)\\ &2&300+3(2)\\ &3&300+3(3)\\ &4&300+3(4)\\ &x&300+3(x) \end{array}\implies y = 300+3x \\\\[-0.35em] ~\dotfill\\\\ \textit{Sally's Salon}\\\\ \begin{array}{cccll} initial~fee&visits&cost\\ \cline{1-3} 250&1&250+5(1)\\ &2&250+5(2)\\ &3&250+5(3)\\ &4&250+5(4)\\ &x&250+5(x) \end{array}\implies y = 250+5x`

when are the plans equal?

`\bf \stackrel{Jim's}{300+3x}~~=~~\stackrel{Sally's}{250+5x}\implies 50+3x=5x \\\\\\ 50=2x\implies \cfrac{50}{2}=x\implies 25=x`