Lesson 3.7 Real-World Problems: Algebraic Reasoning

Transcription

1 Lesson.7 Real-World Problems: Algebraic Reasoning Example Bella has y meters of fabric. She uses meters to make a banner. She then cuts the remaining fabric into pieces in the ratio :. What is the length of the shorter piece of fabric? Method (y ) meters meters y meters Shorter piece Longer piece From the bar model, the length of the shorter piece is: (y ) y Use the distributive property. The shorter piece is y meters. Method Only the remaining cloth is cut into pieces. So, subtract meters from y meters. Shorter piece : Longer piece : So, the shorter piece is the length of the remaining fabric. Length of remaining fabric: y Length of the shorter piece: (y ) y Use the distributive property. The shorter piece is y meters. Reteach Course A 8

2 Complete.. On Monday morning, James walked y + 8 miles from his house to the park. 8 At the park, he jogged times the distance from his house to the park. After his jog, he walked home by the same route. Find the total distance he walked and jogged that morning. Total distance jogged: y ( ) ( ) Use the distributive property. Multiply. He walked and jogged a total distance of meters.. If the average daily rainfall for the last 7 days was (x + 0.) centimeters, write an algebraic expression for the total rainfall for the whole week.. The area of a rectangle is (x + ) square centimeters. The ratio of the shaded region to the unshaded region is :. Write an algebraic expression for the area of the shaded region in terms of x.. A drawer contained 9 pencils and erasers. Will removed p pencils from the drawer. The remaining pencils and erasers were in the ratio :. Write an algebraic expression for the number of pencils left in the drawer. 86 Chapter Lesson.7

3 Solve the word problem by algebraic reasoning. Example Tim is x years old. His father is x 6 years old. His mother is x years younger than his father. Express the sum of their ages in terms of x. Tim's age Father's age Mother's age Sum of their ages: x x 6 x 6 x x x 6 x 6 x x x x x x 0 x 0 x 0 x x The sum of their ages is 8 x years. 0 Write the addition expression. Rewrite the expression. Group like terms. LCM of and is 0. Simplify. Complete.. Adeline has m dollars. Bill has m dollars, and Celia has m 6 dollars more than Bill. Express the total sum of money Adeline, Bill, and Celia have in terms of m. Sum of money: m m ( ) Write the addition expression. m m m m Rewrite the expression. Group like terms. LCM of and is. Simplify. The total sum of money Adeline, Bill, and Celia have is dollars. Reteach Course A 87

4 6. Tiffany read x books last month. Her brother read x books and her 9 sister read x fewer books than Tiffany. Express the total number of books read 9 in terms of x. 7. On a train, there are x adults, q 0 teenagers, and 0 fewer toddlers 6 than adults. How many passengers are on the train? 8. The price of a movie ticket is $7 on a weekday. During the weekend, a movie ticket costs. times the weekday price. During a particular week, m tickets were sold on weekdays and w tickets were sold during the weekend. What is the total amount of money earned from the sale of tickets during that week? 9. One-third of the pears in a basket were rotten. After the rotten pears were thrown away, there were still p pears and q oranges left in the fruit basket. How many total pears and oranges were there in the fruit basket to start with? 88 Chapter Lesson.7

5 Lesson y 8 y (8) y 0 8 He walked and jogged a total distance of y 0 8 miles.. (x.) cm 6. x 9 cm. p 7 pencils. Total sum of money: m m m m d 6 m m m m 6 m m m m m m m m m 0 6 The total sum of money Adeline, Bill, and Celia m 0 have is 6 dollars. 6. (x ) books 7. x q 0 6 passengers 8. (7m 8.w) dollars 9. p q pears and oranges Chapter Lesson.. True. True. True. False. x 6. x 7. y 6 8. y x. x 8. x 0 6. x 0 7. x x x x x Because x x can be rewritten as x, the equations are equivalent. 8. x x x Then check to see if is the solution of the equation x 6. If x, x Because x 6 cannot be rewritten as x, the equations are not equivalent. 9. Yes, they have the same solutions. 0. No, they have different solutions. Lesson.. 6 8x 6 8x 6 6 8x 8 8x x 9 x 9 gives the solution of the equation 6 8x. Check: Substitute 9 for x into the original equation. 6 8x When x 9, the equation 6 8x is true. So x 9 gives the correct solution.. x. y Reteach Course A 6