2 5 An Introduction to Problem Solving Steps

2. 5 An Introduction to Problem Solving

Steps • See table on page 148 and steps on page 149

Number Problem Ex. The sum of five and three times a number is 59. Find the number.

Ex. The sum of five and three times a number is 59. Find the number. x = the # 5 + 3 x = 59 5 + 3 x – 5 = 59 – 5 3 x = 54 3 3 x = 18 the number is 18

Two Unknowns Ex. Page 156, #21: Time spent watching TV exceeded time spent listening to the radio by 581 hours. The combined time devoted to these two media was 2529 hours. In 2007, how many hours did Americans spend listening to radio and how many hours were spent watching TV? (Hint on page 151)

Two Unknowns Ex. Page 156, #21: Time spent watching TV exceeded time spent listening to the radio by 581 hours. The combined time devoted to these two media was 2529 hours. In 2007, how many hours did Americans spend listening to radio and how many hours were spent watching TV? (Hint on page 151) x = time spent listening to radio x + 581 = time spent watching TV x + (x + 581) = 2529 2 x + 581 – 581 = 2529 – 581 2 x = 1948 2 2 x = 974 time spent on radio = 974 hours time spend on TV = 974+581 =1, 555 hours

Consecutive Integers 0 1 2 x x+1 3 4 5 6 1 st consecutive integer = x 2 nd consecutive integer = x + 1

Consecutive Even Integers 0 1 2 x 3 4 5 6 x+2 1 st consecutive even integer = x 2 nd consecutive even integer = x + 2

Consecutive Odd Integers 0 1 x 2 3 4 5 6 x+2 1 st consecutive odd integer = x 2 nd consecutive odd integer = x + 2

Consecutive Integers Ex. Page 156, #28: Babe Ruth and Hank Greenberg are among the ten baseball players with the most home runs in a major league season. The number of home runs by Ruth in 1927 and Greenberg in 1938 are consecutive even integers whose sum is 118. Determine the number of homers hit by Greenberg and by Ruth.

Ex. Page 156, #28: Babe Ruth and Hank Greenberg are among the ten baseball players with the most home runs in a major league season. The number of home runs by Ruth in 1927 and Greenberg in 1938 are consecutive even integers whose sum is 118. Determine the number of homers hit by Greenberg and by Ruth. x = # home runs hit by Greenberg x + 2 = # home runs hit by Ruth x + (x + 2) = 118 2 x + 2 – 2 = 118 – 2 2 x = 116 2 2 x = 58 Greenberg hit 58 home runs Ruth hit 58 +2 or 60 home runs

Base Price Plus Extra “per” Rate Ex. Page, #31: In 2004, mortgage payments averaged $960 per month. From 1975 to 2004, monthly mortgage payments increased by approximately $11. 40 per year. If this trend continues, how many years after 2004 will mortgage payments average $1074? In which year will that occur?

Ex. Page, #31: In 2004, mortgage payments averaged $960 per month. From 1975 to 2004, monthly mortgage payments increased by approximately $11. 40 per year. If this trend continues, how many years after 2004 will mortgage payments average $1074? In which year will that occur? x = # years after 2004 mortgage + increase per year = 1074 960 + 11. 40 x – 960 = 1074 – 960 11. 4 x = 114 11. 4 x = 10 10 years after 2004, so in 2014

Geometry Ex. An American football field is a rectangle with a perimeter of 1040 feet. The length is 200 feet more than the width. Find the width and length of the rectangular field.

Ex. An American football field is a rectangle with a perimeter of 1040 feet. The length is 200 feet more than the width. Find the width and length of the rectangular field. x = width x + 200 = length P = 2 L + 2 W 1040 = 2(x + 200) + 2(x) 1040 = 2 x + 400 + 2 x 1040 = 4 x + 400 1040 – 400 = 4 x + 400 – 400 640 = 4 x 4 4 160 = x x x + 200 width = x = 160 feet length = x + 200 = 160 + 200 = 360 feet

Reduction/Increase Ex. After a 20% reduction, you purchase a television for $320. What was the television’s price before the reduction?

Ex. After a 20% reduction, you purchase a television for $320. What was the television’s price before the reduction? x = original price of TV original price – reduction = new price original price – 20%reduction = new price x – 0. 2 x = 320 1 x – 0. 2 x = 320 0. 8 x = 320 0. 8 x = 400 orig price = x = $400