Question

Paul is paid $75 per week plus $5 for each new gym membership he sells. He may switch to a gym that pays $50 per week and $7.50 for each new membership. How many memberships per week does Paul have to sell for the new gym to be a better deal for him?

Answer 1

For the current gym: Earnings = $75 (weekly base) + $5 (per membership) * x

For the new gym: Earnings = $50 (weekly base) + $7.50 (per membership) * x

$75 + $5x = $50 + $7.50x

Solve for "x":

$25 = $2.50x

x = 10

Paul would need to sell at least 10 new gym memberships per week for the new gym to be a better deal for him.

Answer 2

Paul needs to sell more than 10 new gym memberships per week for the new gym to be a better deal for him.

Explanation:

To determine how many memberships per week Paul needs to sell for the new gym to be a better deal for him, we can set up an equation to compare the earnings from the two options.

Let's denote the number of new gym memberships sold per week as "m".

For Paul's current gym:

Earnings = $75 + $5m

For the new gym:

Earnings = $50 + $7.50m

To find the point at which the new gym becomes a better deal, we need to set up the following inequality:

$50 + $7.50m > $75 + $5m

Now, let's solve the inequality:

$7.50m - $5m > $75 - $50

$2.50m > $25

m > $25 / $2.50

m > 10

Therefore, Paul needs to sell more than 10 new gym memberships per week for the new gym to be a better deal for him.