Linear Equations and Problem Solving Word Problems a

Linear Equations and Problem Solving Word Problems!!! a pic tu re !! aw Keys to succeed! ble Dr va ria Write down important information De fi ne yo ur Put the info in a chart if you can

Consecutive Integers Find three consecutive integers whose sum is 162. Integer 1 Integer 2 Integer 3 Total x-1 x x+1 162

Traveling A pair of hikers, 18 miles apart, begin at the same time to hike toward each other. If one walks at a rate that is 1 mph faster than the other, and if they meet 2 hours later, how fast is each one walking? Hiker 2’s dist. Hiker 1’s dist. 18 Hiker 1’s distance + Hiker 2’s distance = 18 Hiker 1 x 2 2 x Hiker 2 x+1 2 2(x+1) Rate Time Distance = 18

Traveling A pair of cars, 280 miles apart, begin at the same time to run toward each other. If car A from city A runs at a rate that is 10 mph faster than car B from city B, and if they meet 2 hours later, how far is the place they meet away from city A? Car A’s dist. A Car B’s dist. 280 Car A’s distance + Car B’s distance = 280 Car A x + 10 2 2(x + 10) Car B x 2 2 x Rate Time Distance = 280 B

Traveling The Yankee Clipper leaves the pier at 9: 00 am at 8 knots (nautical miles per hour). A half hour later, The Riverboat Rover leaves the same pier in the same direction traveling at 10 knots. At what time will The Riverboat Rovertake The Yankee Clipper? Yankee Clipper 9: 00 ~ 9: 30 Traveled 4 nt. miles 8 x hours after 9: 30 8 x 8 x + 4 Riverboat Rover 9: 00 ~ 9: 30 Traveled 0 nt. miles 10 x hours after 9: 30 10 x 0 + 10 x rate time dist. total Yankee Total = Riverboat Rover Total 4 nt. mi. YC RR 9: 00 8 x nt. mi. YC 10 x nt. mi. 9: 30 YC RR x hr. after 9: 30

Tickets The school play sold 450 tickets for a total of $1160. If student tickets are $2. 00 and adult tickets are $4. 00, how many of each type were sold? Student Adult Total 2 4 ----- x 450 – x 450 2 x 4(450 – x) 1160 Student tickets sales + Adult tickets sales = 1160

Tickets Fred is selling tickets for his home movies. Tickets for friends are $3. 00 and everyone else must pay $5. 00 per ticket. If he sold 72 tickets and made $258 how many of each type did he sell? Friend Non-Friend Total 3 5 ---- x 72 – x 72 3 x 5(72 – x) 258

Accounting Barney has $450 and spends $3 each week. Betty has $120 and saves $8 each week. How many weeks will it take for them to have the same amount of money? Barney 450 3 x 450 – 3 x Betty 120 8 x 120 + 8 x initial wk spend wk end total

You Try This! Accounting Fred has $100 and saves $4 each week. Wilma has $28 and saves $10 each week. How long will it take for them to have the same amount of money? What is that amount? Fred Wilma 100 4 x 28 10 x initial wk sp wk 100 + 4 x 28 + 10 x end total

More on Traveling A driver averaged 50 mph on the highway and 30 mph on the side roads. If the trip of 185 miles took a total of 4 hours and 30 minutes, how many miles were on the highway. Highway Side Road Total 50 30 x 185 – x 185 x/50 (185 – x)/30 4. 5 My God! It is so complicated!!!

More on Consecutive Integers Find three consecutive integers that the difference of the product of two larger ones and the product of two smaller ones is 30. Integer 1 Integer 2 Integer 3 Prod. of Larger 2 Prod. of Smaller 2 x-1 x x+1 x(x + 1) x(x - 1)

More on Traveling A driver averaged 50 mph on the highway and 30 mph on the side roads. If the trip of 185 miles took a total of 4 hours and 30 minutes, how many miles were on the highway. Highway Side Road Total 50 30 x 4. 5 – x 4. 5 50 x 30(4. 5 – x) 185

Weighted Averages You have 32 coins made up of dimes and nickels. You have a total of $2. 85. How many of each type of coin do you have? Dime Nickel Total 10 5 x 32 – x 32 10 x 5(32 – x) 285

Weighted Averages The Quick Mart has two kinds of nuts. Pecans sell for $1. 55 per pound and walnuts sell for $1. 95 per pound. How many pounds of walnuts must be added to 15 pounds of pecans to make a mixture that sells for $1. 75 per pound. Pecans Walnuts Mixture 1. 55 15 15 · 1. 55 1. 95 x 1. 95 x 1. 75 x +15 1. 75(x + 15)

Mixture A druggist must make 20 oz of a 12% saline solution from his supply of 5% and 15% solutions. How much of each should he use? 12% solution 12% 20 20· 12% 5% solution 5% x x · 5% 15% solution 15% 20 – x (20 – x) · 15%