Question

Zoe and Layla sell furniture at competing stores. Each person earns a commission that is proportional to her sales. Zoe earns $150 in commission for every $3,000 in sales. This table shows how Layla's commission depends on her sales:
Layla
Sales Commission
$2,000 $120
$4,000 $240
$6,000 $360
Which person earns more money in commission for every dollar of sales?
How much money would that person earn in commission on $900 in sales?

Answer 1

To determine who earns more money in commission for every dollar of sales, we need to calculate the commission rate for both Zoe and Layla.

**For Zoe:**
Zoe earns $150 in commission for every $3,000 in sales. We can find her commission rate as follows:

\[
\text{Commission Rate (Zoe)} = \frac{\text{Commission}}{\text{Sales}} = \frac{150}{3000} = 0.05
\]

This means that for every dollar of sales, Zoe earns $0.05 in commission.

**For Layla:**
To find Layla's commission rate, we will calculate the commission for different sales amounts in the table provided.

- For $2,000 in sales:
- Commission Rate for $2,000 = \( \frac{120}{2000} = 0.06 \)

- For $4,000 in sales:
- Commission Rate for $4,000 = \( \frac{240}{4000} = 0.06 \)

- For $6,000 in sales:
- Commission Rate for $6,000 = \( \frac{360}{6000} = 0.06 \)

Layla’s commission rate is consistent at 0.06 (or $0.06 for every dollar of sales).

**Comparison of Commission Rates:**
- Zoe: $0.05 per dollar (5%)
- Layla: $0.06 per dollar (6%)

Layla earns more money in commission for every dollar of sales.

**Calculating Commission for $900 in Sales:**
Now, we will calculate how much commission Layla would earn on $900 in sales.

Using Layla’s commission rate:
\[
\text{Commission on \$900 (Layla)} = 0.06 \times 900 = 54
\]

So, Layla would earn $54 in commission on $900 in sales.

**Final Results:**
- Layla earns more at a rate of $0.06 per dollar of sales.
- Layla would earn $54 in commission on $900 in sales.