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Rosa sells cosmetics. She is paid a commission of 3.16% of her first 1500 in sales during the week and 11% on all sales over 1500. What is her commission in a week during which she sells 2137.38 worth of cosmetics? Express your answer as a dollar amount and round to the nearest cent

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ANSWER:

$ 117.51

STEP-BY-STEP EXPLANATION:

The commissions are divided into two payments, the first payment of the first $ 1500 with a commission of 3.16% and a second payment with a commission of 11% of all the remaining money of the first $ 1500.

Therefore, we calculate it as follows:

[tex]\begin{gathered} p_T=p_1+p_2 \\ p_1=1500\cdot\frac{3.16}{100}=47.4 \\ p_2=(2137.38-1500)\cdot\frac{11}{100}=637.38\cdot0.11=70.11 \\ p_T=47.4+70.11 \\ p_T=117.51 \end{gathered}[/tex]

The total commission is $ 117.51

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