Section 3.2 Solving Application Problems
Problem – Solving Procedure • Understand the problem. Identify what is known and what is needed. • Translate the problem into an equation. • Choose a variable to represent one quantity. WRITE IT DOWN. “Let x = …..” • Express all quantities in terms of that variable. • Solve the equation. • Make sure you answer the question that was asked and include units where indicated!
Examples from p 192 - 195 #10. The sum of two consecutive integers is 113. Find the numbers. #14 One number is 5 less than 3 times a second number. Their sum is 43. Find the numbers.
s # 20 The Alpine Valley Ski Shop sold 6 times as many downhill skis as cross-country skis. Determine the number of pairs of cross-country skis sold if the difference in the number of pairs of downhill and cross-country skis sold is 1800. # 22 A candle shop makes 60 candles per week. It plans to increase the number of candles it makes by 8 per week until it reaches a production of 132 candles per week. How many weeks will it take for the shop to reach its productions schedule?
# 28 The amount of time per day spent by 8 – 18 year olds watching tv is 16 minutes more than 5 times then number of minutes they spend reading. If the total amount of time per day reading and watching tv is 274 minutes, determine the number of minutes watching tv. # 34 Carol rents a truck for one day and pays $50 per day plus 30 cents a mile. How far can Carol drive in one day if she has only $92?
# 42 The Coastline Racquet Club has two payment plans for its members. Plan 1 has a monthly fee of $20 plus $8 per hour for court time. Plan 2 has no monthly fee, but court time is $16.25 per hour. If court time is rented in 1-hour intervals, how many hours would you have to play per month so that plan one becomes a better buy? # 48 Yoliette purchased a new car. The cost of the car, including a 7.5% sales tax was $24,600. What was the cost of the car before tax?
# 54 At a 1-day 20% off sale, Jane purchased a hat for $25.99. What is the regular price of the hat? # 56 During the 2006 contract negotiations, the city school board approved a 5% pay increase of its teachers, effective in 2007. If Dana, a first-grade teacher, projects his annual salary to by $46,400, what was is 2006 salary?
# 64 Bill wants to rent a building for a week to show his artwork and has been offered two rental plans. Plan 1 is a rental fee of $500 plus 3% of the dollar sales he makes. Plan 2 is $100 plus 15% of the dollar sales he makes. What dollar sales would result in both plans having the same total cost? # 68 Charles made a $200,000 cash contribution to 2 charities, the American Red Cross and the United Way. The amount received by the Red Cross was 30% greater than the amount received by the United Way. How much did the United Way receive?