Name: _________________________________________ Block



Name: _________________________________________ Block: _____________

Chapter 7: System Word Problems

NOTES

Example:

Randy has some $1 bills and $5 bills in his wallet. He has 15 bills total. When he counts his money he finds that he has $47. How many of each type of bill does Randy have?

STEP 1: Declare what the variables x and y will represent.

X = ______________________________________________________________________

Y = ______________________________________________________________________

STEP 2: Write a system of 2 equations. (Typically one is a $ equation and the other is a total amount equation.)

Equation 1 ($ equation): ______________________________________________________

Equation 2 (total amount): ____________________________________________________

STEP 3: Use substitution, linear combination, or graphing to solve your system.

Write a sentence for your final answer:

System Word Problems:

PRACTICE PROBLEMS

1. Colton is selling hot dogs and hamburgers to earn money for a nice vacation. He is selling hot dogs for $2 each and hamburgers for $5 each. By the end of the day Colton has sold 72 items and earned $180. How many of each item did he sell?

STEP 1: Declare what the variables x and y will represent.

X = ______________________________________________________________________

Y = ______________________________________________________________________

STEP 2: Write a system of 2 equations. (Typically one is a $ equation and the other is a total amount equation.)

Equation 1 ($ equation): ______________________________________________________

Equation 2 (total amount): ____________________________________________________

STEP 3: Use substitution, linear combination, or graphing to solve your system.

Write a sentence for your final answer:

System Word Problems:

PRACTICE PROBLEMS

2. Jason plans on selling 18 portraits at the spring arts festival. The big portraits will cost $25 and the small portraits will cost $10. How many of each did he sell if he made $330?

STEP 1: Declare what the variables x and y will represent.

X = ______________________________________________________________________

Y = ______________________________________________________________________

STEP 2: Write a system of 2 equations. (Typically one is a $ equation and the other is a total amount equation.)

Equation 1 ($ equation): ______________________________________________________

Equation 2 (total amount): ____________________________________________________

STEP 3: Use substitution, linear combination, or graphing to solve your system.

Write a sentence for your final answer:

System Word Problems:

PRACTICE PROBLEMS

3. In one day, the drama club sold 395 tickets for the school play. The center aisle seats were $28 and the sides were $22 per ticket. If the drama club sold $10,130 worth of tickets that day, how many of each type did they sell?

4. You just bought 12 bottles of apple and orange juice for a school dance. The apple juice was on sale for $1 and the orange juice was $1.75 per bottle. If you spent $15 total, how many bottles of each type did you purchase?

System Word Problems:

PRACTICE PROBLEMS

5. Last year you mowed lawns and shoveled driveways at 10 houses in order to make money. You earned $200 per house for mowing the lawn and $180 per house for shoveling the driveway. If you earned $1880 last year, how many lawns did you mow and how many driveways did you shovel?

6. There are sixteen workers employed on a highway project. Some earn $200 per day and others earn $165 per day. The daily payroll is $2745. How many of each type of worker are on the payroll?

System Word Problems:

PRACTICE PROBLEMS

7. In last night’s basketball game Joe had 39 points. He made a total of 16 2-point and 3-point shots. How many of each shot did he have?

8. The Boston Bruins earn one point for every tie and two points for every victory. After 15 games they have not lost a game and have 23 points. How many games have they won and how many games have they tied?

System Word Problems:

PRACTICE PROBLEMS

9. One dozen doughnuts cost $3. One dozen of bagels cost $5. Joe has $20 and wants to feed exactly 72 people (convert to dozens) and he wants to make sure that he has both doughnuts and bagels. Does he have enough money to do so and if he does how many doughnuts and bagels would he buy?

10. Joe has 23 poker chips in his pocket. Some are worth $10 and others are worth $25. When he turns them in he gets $395. How many of each type did he have?

System Word Problems:

PRACTICE PROBLEMS

11. Louise is selling her world famous chili for $2 per cup and $4 per bowl at the parking lot of Gillette Stadium. By day’s end, she has sold 300 items and earned $800. How many bowls and how many cups of chili did she sell?

12. The ice cream man sold 210 items today and made a total profit of $540. The Bomb Pop is his most popular seller and only costs $2. All of his other items are $4. How many Bomb Pops did he sell?

System Word Problems:

PRACTICE PROBLEMS

13. If you work for the Johnson Landscaping crew you either make $100 per day or $150 per day depending on your level of expertise. There are 20 employees who cost a total of $2300 per day. How many employees are at each pay scale?

14. You need twenty bottles of soda but have only $24 to spend. Pepsi products are $1 each but most people would prefer Coke products which are $1.25 each. How many of each will you buy if you wish to buy the least amount of Pepsi products possible?

System Word Problems:

PRACTICE PROBLEMS

15. During a waffle ball game, James was at bat 12 times. Every time that he was at bat he drove in either 3 runs or 1 run. If James drove in a total of 28 runs then how many times at bat did he only drive in one run?

16. Rick has a truck full of 400 recyclable bottles and cans. He receives 5 cents for the cans and 10 cents for the bottles. If he earns 35 dollars (convert it to cents), how many of each did he return?

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download