Serena has job offers from two car dealerships. Classic Cars offers her a base salary of $22,000 per year plus an additional 1% commission on all sales she makes. Sweet Rides offers her a base salary of $13,000 per year plus an additional 2.5% commission on all sales she makes. Determine the amount of car sales in dollars for which both dealerships will pay Serena the same amount. Explain which offer Serena should accept based on the amount of car sales she expects to have.

Serena has job offers from two car dealerships. Classic Cars offers her a base salary of $22,000 per year plus an additional 1% commission on all sales she makes. Sweet Rides offers her a base salary of $13,000 per year plus an additional 2.5% commission on all sales she makes. Determine the amount of car sales in dollars for which both dealerships will pay Serena the same amount. Explain which offer Serena should accept based on the amount of car sales she expects to have.

Question
Ratios, rates, proportions
asked 2020-12-09
Serena has job offers from two car dealerships. Classic Cars offers her a base salary of $22,000 per year plus an additional 1% commission on all sales she makes. Sweet Rides offers her a base salary of $13,000 per year plus an additional 2.5% commission on all sales she makes. Determine the amount of car sales in dollars for which both dealerships will pay Serena the same amount. Explain which offer Serena should accept based on the amount of car sales she expects to have.

Answers (1)

2020-12-10
Let ss be the amount in sales that Serena gets.
Classic Cars offers her a 1% commission on sales so if she makes ss dollars in sales, she will earn 0.01s dollars in commission. She would earn a base salary of $22,000 so her total income would be 22,000+0.01s dollars.
Sweet Rides offers her 2.5% commission so if she makes ss dollars in sales, she will earn 0.025s dollars in commission. She would earn a base salary of $13,000 so her total income would be 13,000+0.025s dollars.
If both dealerships pay her the same, then:
22000+0.01s=13000+0.025s
22000=13000+0.015s
9000=0.015s
600000=s
Serena would then need $600,000 in sales if both dealerships pay her the same amount.
Classic Cars has a higher base salary which means if she makes less than $600,000 in sales, Classic Cars will pay more and if she makes more than $600,000 in sales, Sweet Rides would pay more. Therefore, Serena should accept the offer from Classic Cars if she expects to have less than $600,000 in sales and should accept the offer from Sweet Rides if she expects to have more than $600,000 in sales.
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