2.5 AN INTRODUCTION TO PROBLEM SOLVING

EX1. Three times the difference of a number and 5 is the same as twice the number, decreased by 3. Find the number.

EX2. The sum of three consecutive even integers is 144. Find the integers.

EX3. An 18-foot wire is to be cut so that the longer piece is 5 times longer than the shorter piece. Find the length of each piece.

EX4. Through the year 2000, the state of California had 22 more electoral votes for president than the state of Texas. If the total electoral votes’ for these two states was 86, find the number of electoral votes for each state.

EX5. A car rental agency charges $28 a day and $0.15 a mile. If you rent a car for a day and your bill (before taxes) is $52, how many miles did you drive?

EX6. The measures of two angles of a triangle are equal. If the third angle measures 39 more than each, find the measures of all three angles.

2.6 FORMULAS AND PROBLEM SOLVING

EX1. A family drives from Cincinnati, Ohio to Rapid City, South Dakota, a distance of 1180 miles. They average a rate of 50 miles per hour. How much time did they spend driving?

EX2. A wood deck is being built behind a house. The width of the deck is 14 feet. If there is 168 square feet of decking material, find the length of the deck.

EX3. The length of a rectangle is one more meter than 4 times its width. Find the dimensions if the perimeter is 52 meters.

2.7 PERCENT PROBLEM SOLVING

EX1. The number 22 is what percent of 40?

EX2. If a number decreases from 200 to 120 find the percentage decrease.

EX3. Find the original price of a suit if the sale price is $46 after a 20% discount.

2.8 F URTHER PROBLEM SOLVING

EX1. A jet traveling at 550 mph overtakes a small light plane traveling at 180 that had a 1-hour head start. How far from the starting points are the planes?

EX2. How much 20% dye solution and 50% dye solution should be mixed to obtain 6 liters of a 40% solution?

EX3. Thomas Mason invested part if his $10,000 inheritance in a savings plan that pays 4% simple interest yearly and the rest in a certificate of deposit that pays 6% simple interest yearly at the end of one year, the investment earned $520. Find the amount invested at each rate.