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## Commissions - Sample Math Practice Problems

The math problems below can be generated by MathScore.com, a math practice program for schools and individual families. References to complexity and mode refer to the overall difficulty of the problems as they appear in the main program. In the main program, all problems are automatically graded and the difficulty adapts dynamically based on performance. Answers to these sample questions appear at the bottom of the page. This page does not grade your responses.

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### Complexity=1, Mode=simple

Answer the following questions involving commission.

 1 Maria makes money by commission rates. She gets 15% of everything she sells. If Maria sold \$23000 worth of items this month, what is her salary for the month? 2 Tiffany makes money by commission rates. She gets 21% of everything she sells. If Tiffany sold \$27000 worth of items this month, what is her salary for the month?

### Complexity=1, Mode=withBase

Answer the following questions involving commission.

 1 Peter makes \$7000 a month plus some money by commission rates. He gets 6% of everything he sells. If Peter sold \$55000 worth of items this month, what is his salary for the month? 2 Cindy makes \$9000 a month plus some money by commission rates. She gets 10% of everything she sells. If Cindy sold \$30000 worth of items this month, what is her salary for the month?

### Complexity=1, Mode=earned

Answer the following questions involving commission.

 1 Paul makes a base monthly salary of \$1500. As a vendor, he must sell \$19000 worth of items per month. He also makes a 6% commission on all sales beyond the monthly quota. If Paul sold \$26600 worth of items this month, what is his total salary for the month including base salary and commission to the nearest dollar? 2 Paul makes a base monthly salary of \$1500. As a vendor, he must sell \$20000 worth of items per month. He also makes a 4% commission on all sales beyond the monthly quota. If Paul sold \$26000 worth of items this month, what is his total salary for the month including base salary and commission to the nearest dollar?

### Complexity=1, Mode=bonus

Answer the following questions involving commission.

 1 Jose makes a base monthly salary of \$2700. As a vendor, he must sell \$30000 worth of items per month. He also makes a 10% commission on all sales beyond the monthly quota. There is also an additional 10% bonus on top of the normal commission rate for any sales beyond \$39000. If Jose sold \$42000 worth of items this month, what is his total salary for the month including base salary and commission to the nearest dollar? 2 Cindy makes a base monthly salary of \$3600. As a vendor, she must sell \$35000 worth of items per month. She also makes a 9% commission on all sales beyond the monthly quota. There is also an additional 9% bonus on top of the normal commission rate for any sales beyond \$52500. If Cindy sold \$56000 worth of items this month, what is her total salary for the month including base salary and commission to the nearest dollar?

### Complexity=1, Mode=needed

Answer the following questions involving commission.

 1 Pearl makes a base monthly salary of \$3900. As a vendor, she must sell \$11000 worth of items per month. She also makes a 6% commission on all sales beyond the monthly quota. There is also an additional 3% bonus on top of the normal commission rate for any sales beyond \$17000. If Pearl made \$5500 this month, how much did she sell to the nearest dollar? 2 Steven makes a base monthly salary of \$2700. As a vendor, he must sell \$17000 worth of items per month. He also makes a 10% commission on all sales beyond the monthly quota. There is also an additional 5% bonus on top of the normal commission rate for any sales beyond \$25000. If Steven made \$4800 this month, how much did he sell to the nearest dollar?

### Complexity=1, Mode=simple

Answer the following questions involving commission.

1Maria makes money by commission rates. She gets 15% of everything she sells. If Maria sold \$23000 worth of items this month, what is her salary for the month?
Solution
Amount sold = \$23000
Percentage rate = 15%
Total salary = Amount sold × Percentage rate = \$23000 × (15 / 100) = \$3450
2Tiffany makes money by commission rates. She gets 21% of everything she sells. If Tiffany sold \$27000 worth of items this month, what is her salary for the month?
Solution
Amount sold = \$27000
Percentage rate = 21%
Total salary = Amount sold × Percentage rate = \$27000 × (21 / 100) = \$5670

### Complexity=1, Mode=withBase

Answer the following questions involving commission.

1Peter makes \$7000 a month plus some money by commission rates. He gets 6% of everything he sells. If Peter sold \$55000 worth of items this month, what is his salary for the month?
Solution
Amount sold = \$55000
Percentage rate = 6%
Salary from commission rate = Amount sold × Percentage rate = \$55000 × (6 / 100) = \$3300
Total salary = Base salary + Salary from commission rate = \$7000 + \$3300 = \$10300
2Cindy makes \$9000 a month plus some money by commission rates. She gets 10% of everything she sells. If Cindy sold \$30000 worth of items this month, what is her salary for the month?
Solution
Amount sold = \$30000
Percentage rate = 10%
Salary from commission rate = Amount sold × Percentage rate = \$30000 × (10 / 100) = \$3000
Total salary = Base salary + Salary from commission rate = \$9000 + \$3000 = \$12000

### Complexity=1, Mode=earned

Answer the following questions involving commission.

1Paul makes a base monthly salary of \$1500. As a vendor, he must sell \$19000 worth of items per month. He also makes a 6% commission on all sales beyond the monthly quota. If Paul sold \$26600 worth of items this month, what is his total salary for the month including base salary and commission to the nearest dollar?
Solution
Amount past quota sold = Amount sold - Monthly quota = \$26600 - \$19000 = \$7600
Amount made from commission = Commission Rate × Amount past quota sold = 6 ÷ 100 × \$7600 = \$456
Total amount made = monthly base salary + Amount made from commission = \$1500 + \$456 = \$1956
2Paul makes a base monthly salary of \$1500. As a vendor, he must sell \$20000 worth of items per month. He also makes a 4% commission on all sales beyond the monthly quota. If Paul sold \$26000 worth of items this month, what is his total salary for the month including base salary and commission to the nearest dollar?
Solution
Amount past quota sold = Amount sold - Monthly quota = \$26000 - \$20000 = \$6000
Amount made from commission = Commission Rate × Amount past quota sold = 4 ÷ 100 × \$6000 = \$240
Total amount made = monthly base salary + Amount made from commission = \$1500 + \$240 = \$1740

### Complexity=1, Mode=bonus

Answer the following questions involving commission.

1Jose makes a base monthly salary of \$2700. As a vendor, he must sell \$30000 worth of items per month. He also makes a 10% commission on all sales beyond the monthly quota. There is also an additional 10% bonus on top of the normal commission rate for any sales beyond \$39000. If Jose sold \$42000 worth of items this month, what is his total salary for the month including base salary and commission to the nearest dollar?
Solution
Amount past quota sold = Amount eligible for normal commission rate = Amount sold - Monthly quota = \$42000 - \$30000 = \$12000
Amount past required quota for bonus commission rate = Amount eligible for extra bonus commission rate = Amount sold - required quota for bonus commission rate = \$42000 - \$39000 = \$3000
Amount made from normal commission = Commission Rate × Amount past quota sold = 10 ÷ 100 × \$12000 = \$1200
Amount made from bonus commission = Bonus Commission Rate × Amount past required quota for bonus commission sold = 10 ÷ 100 × \$3000 = \$300
Total amount made = monthly base salary + Amount made from normal commission + Amount made from bonus commission = \$2700 + \$1200 + \$300 = \$4200
2Cindy makes a base monthly salary of \$3600. As a vendor, she must sell \$35000 worth of items per month. She also makes a 9% commission on all sales beyond the monthly quota. There is also an additional 9% bonus on top of the normal commission rate for any sales beyond \$52500. If Cindy sold \$56000 worth of items this month, what is her total salary for the month including base salary and commission to the nearest dollar?
Solution
Amount past quota sold = Amount eligible for normal commission rate = Amount sold - Monthly quota = \$56000 - \$35000 = \$21000
Amount past required quota for bonus commission rate = Amount eligible for extra bonus commission rate = Amount sold - required quota for bonus commission rate = \$56000 - \$52500 = \$3500
Amount made from normal commission = Commission Rate × Amount past quota sold = 9 ÷ 100 × \$21000 = \$1890
Amount made from bonus commission = Bonus Commission Rate × Amount past required quota for bonus commission sold = 9 ÷ 100 × \$3500 = \$315
Total amount made = monthly base salary + Amount made from normal commission + Amount made from bonus commission = \$3600 + \$1890 + \$315 = \$5805

### Complexity=1, Mode=needed

Answer the following questions involving commission.

1Pearl makes a base monthly salary of \$3900. As a vendor, she must sell \$11000 worth of items per month. She also makes a 6% commission on all sales beyond the monthly quota. There is also an additional 3% bonus on top of the normal commission rate for any sales beyond \$17000. If Pearl made \$5500 this month, how much did she sell to the nearest dollar?
Solution
Start by guessing Pearl didn't sell enough to garner any salary from the bonus commission rate.
Salary made from commission = Total salary - monthly base salary = \$5500 - \$3900 = \$1600
Commission rate × Amount eligible for commission rate = Amount earned from commission = Rate × Amount = Salary
Amount = Salary ÷ Rate = \$1600 ÷ (6 / 100) = \$26667
So presuming no bonus commission is made, Pearl would have to sell \$11000 + \$26667 = \$37667
Since the guessed amount sold is more than the required quota for obtaining bonus commission, our guess was wrong and we know that Pearl sold at least the required quota for obtaining bonus commission which is \$17000.
Amount made from commission for sales below \$17000 = Amount below \$17000 eligible for normal commission × normal commission rate = \$6000 × 6 / 100 = \$360
Amount left to make from bonus commission = Total salary - monthly base salary - amount made from normal commission for sales below \$17000 = \$5500 - \$3900 - \$360 = \$1240
Total commission percentage rate for sales over \$17000 = normal commission percentage rate + bonus commission percentage rate = 6% + 3% = 9%
Again for the money made from bonus commission, Amount = Salary / Rate = \$1240 / (9 / 100) = \$13778
Total amount sold = monthly quota + amount sold at only normal commission + amount sold at bonus commission = \$11000 + \$6000 + \$13778 = \$30778
2Steven makes a base monthly salary of \$2700. As a vendor, he must sell \$17000 worth of items per month. He also makes a 10% commission on all sales beyond the monthly quota. There is also an additional 5% bonus on top of the normal commission rate for any sales beyond \$25000. If Steven made \$4800 this month, how much did he sell to the nearest dollar?
Solution
Start by guessing Steven didn't sell enough to garner any salary from the bonus commission rate.
Salary made from commission = Total salary - monthly base salary = \$4800 - \$2700 = \$2100
Commission rate × Amount eligible for commission rate = Amount earned from commission = Rate × Amount = Salary
Amount = Salary ÷ Rate = \$2100 ÷ (10 / 100) = \$21000
So presuming no bonus commission is made, Steven would have to sell \$17000 + \$21000 = \$38000
Since the guessed amount sold is more than the required quota for obtaining bonus commission, our guess was wrong and we know that Steven sold at least the required quota for obtaining bonus commission which is \$25000.
Amount made from commission for sales below \$25000 = Amount below \$25000 eligible for normal commission × normal commission rate = \$8000 × 10 / 100 = \$800
Amount left to make from bonus commission = Total salary - monthly base salary - amount made from normal commission for sales below \$25000 = \$4800 - \$2700 - \$800 = \$1300
Total commission percentage rate for sales over \$25000 = normal commission percentage rate + bonus commission percentage rate = 10% + 5% = 15%
Again for the money made from bonus commission, Amount = Salary / Rate = \$1300 / (15 / 100) = \$8667
Total amount sold = monthly quota + amount sold at only normal commission + amount sold at bonus commission = \$17000 + \$8000 + \$8667 = \$33667