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

We will meet the following typical types of real-life application questions: Consecutive Integers Geometry Traveling Tickets Accounting The real-life application questions are not just limited to the those above types. Others may be: 6. Clock (combination of Geometry and Traveling) 7. Work 8. Mixture

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

Consecutive Integers x - 2 x You Try This! 2) The measures of the angles of a certain triangle are consecutive even integers. Find their measures. Angle 1 x - 2 Angle 2 x Angle 3 x + 2 Total 180 1 2 3

Geometry 3) A board is 12 ft long and is to be cut into 3 pieces so that the second piece is twice the size of the first piece, and the third is three times the size of the second piece. Find the length of the 3 pieces of board. 1 2 3 Analysis: second = 2 · first, third = 3 · second = 3 · (2 · first) = 6 · first Piece 1 x Piece 2 2x Piece 3 6x

You Try This! Geometry 4) The longest side of a triangle is 3 inches more than twice the middle side. The shortest side is 2 inches less than the middle side. If the perimeter is 45 inches, how long is each side? Longest 2x+3 Middle x Shortest x – 2 Perimeter 45 2x+3 x-2 x

Traveling 5) 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 1’s dist. Hiker 2’s dist. 18 Hiker 1’s distance + Hiker 2’s distance = 18 Hiker 1 x 2 2x Hiker 2 x+1 2(x+1) Rate Time Distance = 18

Traveling You Try This! 6) 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. Car B’s dist. 280 A B Car A’s distance + Car B’s distance = 280 Car A x + 10 2 2(x + 10) Car B x 2x Rate Time Distance = 280

Traveling 7) 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 8 x hours after 9:30 8x 8x + 4 Riverboat Rover 0 nt. miles 10 10x 0 + 10x rate time dist. total Yankee Total = Riverboat Rover Total 4 nt. mi. 8x nt. mi. YC YC YC RR 10x nt. mi. RR x hr. after 9:30 9:00 9:30

Tickets 2 x 2x 4 450 – x 4(450 – x) ----- 450 1160 8) 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 2 x 2x Adult 4 450 – x 4(450 – x) Total ----- 450 1160 Student tickets sales + Adult tickets sales = 1160

Tickets 3 x 3x 5 72 – x 5(72 – x) 72 258 You Try This! 9) 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 3 x 3x Non-Friend 5 72 – x 5(72 – x) Total ---- 72 258

Accounting 10) 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 – 3x Betty 120 8 120 + 8x initial wk spend wk end total

Accounting 100 4 x 100 + 4x 28 10 28 + 10x initial wk sp wk end total You Try This! 11) 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 100 4 x 100 + 4x Wilma 28 10 28 + 10x initial wk sp wk end total

More on Consecutive Integers 12) 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)

More on Traveling 13) 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 50 x x/50 Side Road 30 185 – x (185 – x)/30 Total 185 4.5 My God! It is so complicated!!!

More on Traveling 50 x 50x 30 4.5 – x 30(4.5 – x) 4.5 185 13) 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 50 x 50x Side Road 30 4.5 – x 30(4.5 – x) Total 4.5 185

Weighted Averages 14) 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 10 x 10x Nickel 5 32 – x 5(32 – x) Total 32 285

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

Mixture 16) 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%