Solving linear equations for grade 8.ppt

A presentation for solving linear equations

1. Linear Equations and Problem Solving
Word Problems!!!
Keys to succeed!
Write down important information
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Put the info in a chart if you can
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2. Find three consecutive integers whose sum is
162.
Consecutive Integers
Integer 1x - 1
Integer 2x
Integer 3x + 1
Total 162
1 1 162x x x    
3 162x
54x
1 54 1 53x   
1 54 1 55x   

3. 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 1x 2 2x
Hiker 2x+1 2 2(x+1)
RateTime Distance = 18
2 2( 1) 18x x  
2 2 2 18x x  
4 2 18x 
4 16x
4 mphx
1 4 1 5 mphx   
Traveling
Hiker 1’s distance + Hiker 2’s distance = 18
Hiker 1’s dist.
Hiker 2’s dist.
18

4. 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 + 10 2 2(x + 10)
Car B x 2 2x
RateTime Distance = 280
2 2( 10) 280x x  
2 2 20 280x x  
4 20 280x 
4 260x
65 mphx
10 75 mphx 
Traveling
Car A’s distance + Car B’s distance = 280
Car A’s dist. Car B’s dist.
280
A B
2( 10) 275 150 mi.x  

5. 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
9:00 ~ 9:30
Traveled
0 nt. miles
10 x hours after
9:30
10x0 + 10x
rate time dist.total
4 8 0 10x x  
4 2x
2 hr.x
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

6. 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
2 4(450 ) 1160x x  
2 1800 4 1160x x  
2 640x 
320 tksx
2 1800 1160x  
450 450 320 130 tksx   
Tickets
Student tickets sales + Adult tickets sales = 1160

7. 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-Friend5 72 – x 5(72 – x)
Total ---- 72 258
3 5(72 ) 258x x  
3 360 5 258x x  
2 102x 
51 tksx
2 360 258x  
72 72 51 21 tksx   
Tickets

8. 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?
Barney450 3 x 450 – 3x
Betty120 8 x 120 + 8x
initialwk spendwk end total
450 3 120 8x x  
450 120 11x 
3 wkx
330 11x
Accounting

9. Fred 100 4 x100 + 4x
Wilma 28 10 x28 + 10x
initialwk sp wkend total
100 4 28 10x x  
100 28 6x 
12 wkx
72 6x
Accounting
You Try This!
28 10 28 1012 $148x    
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?

10. 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 50 x x/50
Side Road 30185 – x (185 – x)/30
Total 185 4.5
185
4.5
50 30
x x
  My God! It is so complicated!!!

11. 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 2x(x + 1)
Prod. of Smaller 2x(x - 1)
( 1) ( 1) 30x x x x   
2 2
30x x x x   
2 30x
15x
1 16x 
1 14x 

12. Highway 50 x 50x
Side Road 304.5 – x 30(4.5 – x)
Total 4.5 185
50 30(4.5 ) 185x x  
50 135 30 185x x  
20 135 185x 
20 50x
2.5 hr.x
50 50(2.5) 125 mi.x 
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

13. 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 10 x 10x
Nickel 532 – x

5(32 – x)
Total 32 285
10 5(32 ) 285x x  
10 160 5 285x x  
5 160 285x 
5 125x
25x
32 7x 

14. 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.
Pecans1.5515 15 · 1.55
Walnuts1.95x 1.95x
Mixture1.75x +15 1.75(x + 15)
1.55 15 1.95 1.75( 15)x x   
23.25 1.95 1.75 26.25x x  
23.25 0.2 26.25x 
0.2 3x
15 lb.x
Weighted Averages

15. 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%
20 0.12 0.05 (20 ) 0.15x x    
2.4 0.05 3 0.15x x  
0.6 0.1x 
6 oz.x
2.4 0.1 3x 
Mixture
20 20 6 14 oz.x   