1. 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

2. 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

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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. Tickets 2 x 2x 4 450 – x 4(450 – x) ----- 450 1160
8) The school play sold 450 tickets for a total of $ 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

11. 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

12. 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 x
initial
wk spend wk
end total

13. 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 x
Wilma 28 10 x
initial
wk sp wk
end total

14. 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)

15. 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!!!

16. 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

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

18. 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)

19. 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%