Final answer:
Martin will earn more money than Hanna when he sells more than 7 jerseys, as determined by comparing their earnings equations and solving the resulting inequality.
Step-by-step explanation:
The question asks us to determine when Martin will make more money than Hanna based on their weekly earnings plus the commission they make for each jersey sold. To approach this question, we can set up an equation where Hanna's earnings are represented as $150 + $3x, with 'x' being the number of jerseys sold, and Martin's earnings as $136 + $5x.
We want to find the point where Martin's earnings exceed Hanna's, which can be expressed as the inequality $136 + $5x > $150 + $3x. Solving this inequality involves subtracting $136 and $3x from both sides, which gives us $2x > $14. Dividing both sides by 2, we get x > 7. Therefore, Martin needs to sell more than 7 jerseys to earn more than Hanna.
This mathematical problem is about understanding linear equations and inequalities and applying these concepts to solve real-world problems. Using mathematics to analyze earnings and performance targets is a common problem-solving skill in business and economics.