Linear Equations and Problem Solving Word Problems!!! Keys to succeed! Write down important information Draw a picture Put the info in a chart if you can Define your variable!!

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

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 1x22x Hiker 2x+122(x+1) RateTimeDistance = 18 Traveling Hiker 1’s distance + Hiker 2’s distance = 18 Hiker 1’s dist. Hiker 2’s dist. 18

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 Ax (x + 10) Car Bx22x RateTimeDistance = 280 Traveling Car A’s distance + Car B’s distance = 280 Car A’s dist. Car B’s dist. 280 A B

The Yankee Clipper leaves the pier at 9:00am 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 Rover overtake The Yankee Clipper? Yankee Clipper 9:00 ~ 9:30 Traveled 4 nt. miles 8x hours after 9:30 8x8x + 4 Riverboat Rover 9:00 ~ 9:30 Traveled 0 nt. miles 10x hours after 9:30 10x0 + 10x ratetimedist.total Yankee Total = Riverboat Rover Total Traveling 4 nt. mi. RR YC RR YC 10x nt. mi. 8x nt. mi. YC 9:00 9:30 x hr. after 9:30

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 2x2x Adult 4450 – x4(450 – x) Total Tickets Student tickets sales + Adult tickets sales = 1160

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 3x3x Non-Friend 572 – x5(72 – x) Total Tickets

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 4503x450 – 3x Betty 1208x x initialwk spendwkend total Accounting

Fred 1004x x Wilma 2810x x initialwk spwkend total Accounting You Try This! 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?

More on Traveling A driver averaged 50mph on the highway and 30mph 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 50xx/50 Side Road – x(185 – x)/30 Total 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 x - 1 Integer 2 x Integer 3 x + 1 Prod. of Larger 2 x(x + 1) Prod. of Smaller 2 x(x - 1)

Highway 50x50x Side Road – x30(4.5 – x) Total A driver averaged 50mph on the highway and 30mph 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. More on Traveling

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 10x10x Nickel 532 – x5(32 – x) Total 32285

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 · 1.55 Walnuts 1.95x1.95x Mixture 1.75x (x + 15) Weighted Averages

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%2020·12% 5% solution 5%xx · 5% 15% solution 15%20 – x(20 – x) ·15% Mixture