Question
Bia earns a commission on the sales she makes each month. Within a month, Bia earns a
3%
commission on the first
$3000
she has in sales. She earns a
4.5%
commission on the amount of her sales that are greater than
$3000
.
Part A
Last month, Bia had
$5000
in sales. How much money did she earn in commission?
Enter a number in the box.
$
Question 2
Part B
This month, Bia earned
$157.50
in commission. How much money did she have in sales?
Enter a number in the box.
3%
commission on the first
$3000
she has in sales. She earns a
4.5%
commission on the amount of her sales that are greater than
$3000
.
Part A
Last month, Bia had
$5000
in sales. How much money did she earn in commission?
Enter a number in the box.
$
Question 2
Part B
This month, Bia earned
$157.50
in commission. How much money did she have in sales?
Enter a number in the box.
Answers
GPT-4o mini
To calculate Bia's commission for both parts of the question, we can break it down step by step.
**Part A:**
Bia had $5000 in sales for last month.
1. First, we calculate her commission for the first $3000:
\[
\text{Commission for first } \$3000 = 0.03 \times 3000 = 90
\]
2. Next, we calculate her commission for the amount over $3000:
\[
\text{Amount over } \$3000 = 5000 - 3000 = 2000
\]
\[
\text{Commission for amount over } \$3000 = 0.045 \times 2000 = 90
\]
3. Now, we add both commissions together:
\[
\text{Total commission} = 90 + 90 = 180
\]
So, for Part A, Bia earned **$180** in commission last month.
**Part B:**
This month, Bia earned $157.50 in commission. We need to find out how much her sales were.
Let \( x \) be the total sales this month.
1. If \( x \) is less than or equal to $3000, her commission would be:
\[
0.03x = 157.50
\]
Solving for \( x \):
\[
x = \frac{157.50}{0.03} = 5250
\]
This is not possible since it exceeds $3000.
2. Therefore, \( x \) must be greater than $3000. We can set up the equation for the commission:
\[
\text{Commission on the first } 3000 = 90
\]
We denote the amount of sales over $3000 as \( y \) (where \( y = x - 3000 \)):
\[
\text{Commission on amount over } 3000 = 0.045y
\]
So we have:
\[
90 + 0.045y = 157.50
\]
3. Simplifying:
\[
0.045y = 157.50 - 90
\]
\[
0.045y = 67.50
\]
\[
y = \frac{67.50}{0.045} = 1500
\]
4. Now, we calculate the total sales:
\[
x = 3000 + y = 3000 + 1500 = 4500
\]
So, for Part B, Bia had **$4500** in sales this month.
Final Answers:
- Part A: **$180**
- Part B: **$4500**
**Part A:**
Bia had $5000 in sales for last month.
1. First, we calculate her commission for the first $3000:
\[
\text{Commission for first } \$3000 = 0.03 \times 3000 = 90
\]
2. Next, we calculate her commission for the amount over $3000:
\[
\text{Amount over } \$3000 = 5000 - 3000 = 2000
\]
\[
\text{Commission for amount over } \$3000 = 0.045 \times 2000 = 90
\]
3. Now, we add both commissions together:
\[
\text{Total commission} = 90 + 90 = 180
\]
So, for Part A, Bia earned **$180** in commission last month.
**Part B:**
This month, Bia earned $157.50 in commission. We need to find out how much her sales were.
Let \( x \) be the total sales this month.
1. If \( x \) is less than or equal to $3000, her commission would be:
\[
0.03x = 157.50
\]
Solving for \( x \):
\[
x = \frac{157.50}{0.03} = 5250
\]
This is not possible since it exceeds $3000.
2. Therefore, \( x \) must be greater than $3000. We can set up the equation for the commission:
\[
\text{Commission on the first } 3000 = 90
\]
We denote the amount of sales over $3000 as \( y \) (where \( y = x - 3000 \)):
\[
\text{Commission on amount over } 3000 = 0.045y
\]
So we have:
\[
90 + 0.045y = 157.50
\]
3. Simplifying:
\[
0.045y = 157.50 - 90
\]
\[
0.045y = 67.50
\]
\[
y = \frac{67.50}{0.045} = 1500
\]
4. Now, we calculate the total sales:
\[
x = 3000 + y = 3000 + 1500 = 4500
\]
So, for Part B, Bia had **$4500** in sales this month.
Final Answers:
- Part A: **$180**
- Part B: **$4500**