Solving real-world problems using systems of equations

Transcription

1 May 15, 2013 Solving real-world problems using systems of equations page 1 Solving real-world problems using systems of equations Directions: Each of these problems can be represented using a system of two equations. You can answer the question by solving the system (that is, finding the intersection of two graphs). 1. In basketball, some baskets are worth 3 points and others are worth 2 points. Suppose that a player makes 7 baskets, and scores a total of 18 points. How many of the baskets were two-point baskets, and how many were three-point baskets? Variables: System: x + y = 7 3x + 2y = 18 x = number of three-point baskets y = number of two-point baskets Rewrite the first equation as y = Rewrite the second equation as y = x + y = 7 3x + 2y = 18 Graph both equations (by yourself, no calculator). Solution Final answer (Please write a full sentence that tells how many of each kind of basket.)

2 May 15, 2013 Solving real-world problems using systems of equations page 2 2. A sub sandwich shop sells small subs and large subs. One customer buys 1 small sub and 2 large subs for $10. Another customer buys 2 small subs and 1 large sub for $8. What are the prices for a small sub and a large sub? Variables: x = price of an small sub y = price of a large sub Rewrite the first equation. Rewrite the second equation. Graph both equations (by yourself, no calculator). Solution Final answer (Please write a full sentence that tells the price of each kind of sub.)

3 May 15, 2013 Solving real-world problems using systems of equations page 3 3. A store sells sweaters for $40 each, and jeans for $20 each. Maria buys 5 pieces of clothing (some jeans and some sweaters), and pays $160. How many sweaters and how many jeans did she buy? Write word descriptions of the two variables in this problem. x = y = Graph both equations (by yourself, no calculator). Solution Final answer (full sentence)

4 May 15, 2013 Solving real-world problems using systems of equations page 4 4. A fast-food restaurant sells burgers and fries. One customer buys 3 burgers and 2 fries, and pays $7.15. Another customer buys 4 burgers and 3 fries, and pays $9.93. What are the selling prices for burgers and fries? Write word descriptions of the two variables in this problem. x = y = Rewrite the first equation. Rewrite the second equation. Graph both equations (use calculator). Solution from calculator ( ) Final answer (full sentence)

5 May 15, 2013 Solving real-world problems using systems of equations page 5 5. Xena and Yvonne are sisters. Xena s age and Yvonne s age add up to 30. Yvonne is four years older than Xena. How old are the sisters? Write word descriptions of the two variables in this problem. x = y = Hint: The equations come from the two underlined parts of the problem. Rewrite the first equation. Rewrite the second equation. Graph both equations on calculator. Before graphing, press and enter the numbers shown here. Solution from calculator Check solution in the first equation Check solution in the second equation Final answer (full sentence)

6 May 15, 2013 Solving real-world problems using systems of equations page 6 6. You have some quarters and some nickels in your pocket. In total, you have 7 coins, and together they are worth 95 cents. How many are nickels and how many are quarters? Write word descriptions of the two variables in this problem. x = y = Hint: The equations come from the two underlined parts of the problem. Rewrite the first equation. Rewrite the second equation. Graph both equations on calculator. Before graphing, press to get back to the normal graphing window. Solution from calculator Final answer (full sentence)

7 May 15, 2013 Solving real-world problems using systems of equations page 7 For the last two problems, I ve taken away the hints about what steps to follow, but keep solving the problems in the same way. You decide whether to graph on paper or on the calculator. Remember to check your answers. 7. A music store sells tapes for $10 and CD s for $15. Someone buys 5 items in this store, and pays $60. How many of these items were tapes, and how many were CD s?

8 May 15, 2013 Solving real-world problems using systems of equations page 8 8. In Mrs. Smith s Kindergarten, there are 20 students. The number of girls is 4 less than the number of boys. How many girls and how many boys are there?