Write and Solve Systems of Equations

Write and Solve Systems of Equations

Name: ______Date: ______

Directions: For each problem label the variables, write a system of equations, solve the system and then answer the question.

1. The total cost of 15 gallons of regular unleaded gasoline and 10 gallons of premium unleaded gasoline is $35.50. Premium unleaded costs $0.20 more per gallon than regular unleaded. What is the cost per gallon of each type of gasoline?

2. You and a friend go to a Mexican food restaurant. You order 2 tacos and 3 enchiladas and your friend orders 3 tacos and 5 enchiladas! Your bill was $7.80 plus tax, and your friend’s bill was $12.70 plus tax. How much was each taco and each enchilada?

3. You are buying decorations for a birthday party. The before-tax total for 3 rolls of crepe paper and 20 balloons is $11.40. After you start decorating, you need more supplies. You buy 2 more rolls of crepe paper and 10 more balloons for $7.20. How much did each roll of crepe paper and each balloon cost?

4. A total of $8,000 is invested in two funds pay 4% and 5% annual interest. The combined annual interest is $350. How much of the $8,000 is invested in each fund?

5. Julia is making candles. In the morning she made 9 rose candle plates and 6 lily candle plates. They had a total of 48 candles. In the evening, she made 6 rose candle plates and 12 lily candle plates. They had a total of 72 candles. How many candles are on the rose plates? How many candles are on the lily plates?

6. Elaine wants to purchase books. On Monday she purchased 5 red bags of books and 9 blue bags of books for a total of 78 books. On Tuesday she purchased 7 red bags of books and 4 blue bags of books for a total of 49 books. How many books were in the red bags and in the blue bags?

7. Jacob wants to make fruit juice. On Tuesday he buys 8 packets of orange and 6 packets of apple juice. The packets make a total of 34 cups of fruit juice. On Wednesday he buys 14 packets of orange and 6 packets of apple. This allows him to make 46 cups of fruit juice. How many cups can one packet of orange juice make? How many cups can one packet of apple juice make?

8. Daniel wants to make snack plates of chips. The chips are 6 inches in length each. On Saturday he made 5 plates of potato chips and 9 plates of tomato chips, for a total of 94 chips. On Sunday he made 5 plates of potato chips and 4 plates of tomato chips for a total of 64 chips. How many chips are on the potato chip plates? How many chips are on the tomato chip plates?

9. Your wonderful math teacher is giving a test worth 200 points. There are 46 three-point and five-point questions. How many of each are on the test?