Question

challenging financial math worksheet: commission - based and piecework pay
solve the following word problems carefully. show all steps in your work, including setting up equations where needed. these problems are designed to challenge your critical thinking and application of financial math concepts.

1. a salesperson earns a base salary of $500 per week plus a 7% commission on sales. if they want to earn at least $1,250 in one week, what must their minimum sales be?
2. a worker is paid $2.75 per unit assembled. if their weekly goal is to earn at least $660, how many units must they assemble?
3. a real estate agent earns a 2.5% commission on the sale of houses. if they sell three houses priced at $180,000, $220,000, and $260,000, what is their total commission?
4. a furniture salesperson earns 6% commission on sales up to $10,000 in a month and 8% commission on sales above $10,000. if they sell $15,000 worth of furniture, how much commission do they earn?
5. a factory worker earns $0.85 per product made up to 500 products, and $1.10 for each product after that in a week. if the worker produces 780 products, what is their total pay?
6. a car dealer earns a $400 bonus for each car sold, plus a 5% commission on the total sales price. if they sell 4 cars at $18,000 each, what is their total earnings for that week?
7. a company pays its sales staff the greater of either a $700 fixed weekly salary or 9% commission on sales. if a salesperson sells $6,500 worth of products in a week, which pay option should they take?
8. a factory pays workers $1.50 per gadget produced. however, if a worker produces more than 1,000 gadgets in a month, they receive an additional $0.25 per gadget for the entire batch. if a worker makes 1,120 gadgets, what is their total pay?
9. a jewelry store employee earns 4% commission on items sold. in one week, they sell $12,000 worth of diamond rings and $8,000 worth of gold necklaces. if their store requires them to split commissions equally with an assistant, how much does each person get?
10. a salesperson earns $1,000 in base pay per month and 10% commission on sales. however, if sales exceed $20,000 in a month, the commission rate increases to 12% on the total amount. how much will the salesperson earn in a month if their sales total $25,000?

Explanation:

1.

Step1: Set up the equation

Let $x$ be the amount of sales. The total earnings $E$ is the base - salary plus the commission. So, $E = 500+0.07x$. We want $E\geq1250$, so the equation is $500 + 0.07x\geq1250$.

Step2: Solve for $x$

Subtract 500 from both sides: $0.07x\geq1250 - 500=750$. Then divide both sides by 0.07: $x\geq\frac{750}{0.07}\approx10714.29$.

Step1: Set up the equation

Let $n$ be the number of units assembled. The total pay $P$ is given by $P = 2.75n$. We want $P\geq660$. So the equation is $2.75n\geq660$.

Step2: Solve for $n$

Divide both sides by 2.75: $n\geq\frac{660}{2.75}=240$.

Step1: Calculate the total value of houses sold

The total value of the three houses is $V=180000 + 220000+260000=660000$.

Step2: Calculate the commission

The commission $C$ is 2.5% of $V$. So $C = 0.025\times660000 = 16500$.

Answer:

At least $\$10714.29$

2.