7.4 Applications of Linear Systems

Transcription

1 7.4 Applications of Linear Systems 1. Anthony and Anne bought some pens and pencils. Anthony bought 4 pens and 5 pencils, which cost him $6.71. Anne bought 5 pens and 3 pencils, which cost her $7.12. Let x equal the price of a pen. Let y equal the price of a pencil. a. Write an equation that relates the number of pens and pencils Anthony bought to the amount he paid for them. b. Write an equation that relates the number of pens and pencils Anne bought to the amount she paid for them. c. Solve the system you wrote for parts (a) and (b) to find the price of a pen and the price of a pencil. 1

2 2. Suppose you bought supplies for a party. Three rolls of streamers and 15 party hats cost $30. Later, you bought 2 rolls of streamers and 4 party hats for $11. How much did each roll of streamers cost? How much did each party hat cost? x= y= 2

3 2. Suppose you bought supplies for a party. Three rolls of streamers and 15 party hats cost $30. Later, you bought 2 rolls of streamers and 4 party hats for $11. How much did each roll of streamers cost? How much did each party hat cost? streamers hats Answer streamers cost $2.50 hats cost $1.50 3x+22.5 = x=

4 3. The Math Club and the Science Club had fundraisers to buy supplies for a local food pantry. The math club spent $135 buying six cases of juice and one case of bottled water. The science club spent $110 buying four cases of juice and two cases of bottled water. How much did a case of juice cost? How much did a case of bottled water cost? x= y= Answer 4

5 3. The Math Club and the Science Club had fundraisers to buy supplies for a local food pantry. The math club spent $135 buying six cases of juice and one case of bottled water. The science club spent $110 buying four cases of juice and two cases of bottled water. How much did a case of juice cost? How much did a case of bottled water cost? x=juice y=water Answer juice costs water costs 4x= x=20 5

6 4. Suppose you bought supplies for a party. Three rolls of streamers and 14 party hats cost $40. Later, you bought 2 rolls of streamers and 4 party hats for $16. How much did each roll of streamers cost? How much did each party hat cost? x= y= streamers cost hats cost 6

7 4. Suppose you bought supplies for a party. Three rolls of streamers and 14 party hats cost $40. Later, you bought 2 rolls of streamers and 4 party hats for $16. How much did each roll of streamers cost? How much did each party hat cost? x= y= streamers cost hats cost 7

8 9. The sum of two numbers is 32. Their difference is 8. Write a system of equations that describes this situation and then solve to find the two numbers. 8

9 9. The sum of two numbers is 32. Their difference is 8. Write a system of equations that describes this situation and then solve to find the two numbers. 9

10 10. The sum of two numbers is 50. Their difference is 20. Write a system of equations that describes this situation and then solve to find the two numbers. 10

11 10. The sum of two numbers is 50. Their difference is 20. Write a system of equations that describes this situation and then solve to find the two numbers. y= 2nd number option 1 for how to write answer The first number is 35 the second number is 15 2x = x = 35 x + y = y = y = 15 option 2 for how to write answer The numbers are 35 and 15 11

12 Homework: Complete HW sheet problems #1 4 and #8 10 Show work like we did in the notes. Do the work in your notebook or on looseleaf. Your choice. Bring HW back on Monday to show me. 12