Question

A certain salesman's yearly income is determined by a base salary plus a commission on the sales he makes during the year. Did the salesman's base salary account for more than half of the salesman's yearly income last year?

If the amount of the commission had been 30 percent higher, the salesman's income would have been 10 percent higher last year.

Answer 1

By setting up an equation with the base salary as B and the commission as C, we find that the base salary is twice that of the commission. Therefore, the base salary accounts for more than half of the salesman's yearly income.

Step-by-step explanation:

To determine if the salesman's base salary was more than half of his yearly income, we can use the information provided: a 30 percent increase in commission would result in a 10 percent higher total income. Let's call the base salary B and the commission C. The total income is B + C, and if the commission were increased by 30 percent, the total income would be B + 1.3C.

A 10 percent increase in total income implies that B + 1.3C = 1.1(B + C). Simplifying this equation gives us 1.3C = 1.1B + 1.1C, which reduces to 0.2C = 0.1B, or 2C = B. This means the base salary is twice that of the commission, so the base salary indeed accounts for more than half of the salesman's yearly income.