Question

Pre-calc word problem

You receive two sales job offers. One company offers a straight commission of 5% of sales. The other company offers a salary of $500 per week plus 2% of sales. How much would you have to sell in a week in order to make the straight commission job offer better? (Round your answer to the nearest cent.)
To make straight commission the better offer, you would have to sell (more than, less than, equal to) $____ per week.

Answer 1

More than $16,666.67.

Explanation:

Define the variables:

• Let x = Weekly sales (in dollars).
• Let y = Total salary (in dollars).

Create an equation for each job offer using the defined variables and given information.

Job Offer 1

Straight commission of 5% of sales:

`\implies y=0.05x`

Job Offer 2

A salary of $500 per week plus 2% of sales:

`\implies y=500+0.02x`

For Job Offer 1 to be better, set the expression for this offer to be greater than the expression for Job Offer 2 and solve the inequality:

`\implies 0.05x > 500+0.02x`

`\implies 0.05x-0.02x > 500+0.02x-0.02x`

`\implies 0.03x > 500`

`\implies (0.03x)/(0.03) > (500)/(0.03)`

`\implies x > 16666.66666...`

Therefore, to make straight commission (Job Offer 1) the better offer, you would have to sell more than $16,666.67 (nearest cent) per week.

Answer 2

To make straight commission the better offer, you would have to sell more than $16666.67 per week.

Explanation:

Set inequality, assuming the sales amount is x:

• 5% of x > 500 + 2% of x

• 0.05x > 500 + 0.02x
• 0.05x - 0.02x > 500
• 0.03x > 500
• x > 500/0.03
• x > 16666.67 (rounded to the nearest cent)