Algebra Word Problems
Lesson 9
Worksheet 9
Algebra Word Problems
Involving
Levers
1
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Algebra Word Problems – Lesson 9, Worksheet 9, Algebra Word Problems
Involving Levers
Problem 1) Jacob weighs 90 pounds and sits 6 feet from the fulcrum of a
seesaw. If Sally weighs 120 pounds and sits on the other side, how many feet
from the fulcrum must she sit to have the seesaw balance?
Problem 2)
At one end of a lever is a 14 kg weight which is 9 meters from the
fulcrum. How much weight, in kg, should be placed on the other end 18 meters
from the fulcrum to balance?
Problem 3)
A person places a lever under a 240 pound weight that is 6 feet
from the fulcrum. In order to lift the rock, how much force must the person on
the other end of the lever, if he is 9 feet from the fulcrum?
2
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Problem 4)
Where should the fulcrum, in feet, be placed under a 12 meter
lever if there is a 24 kg weight on one end and a 36 kg weight on the other end in
order to balance?
Problem 5) Brian weighs 56 kg and sits 1.8 meters from the fulcrum of a
seesaw. If Lisa weighs 48 kg and sits on the other side, how far, in meters, from
the fulcrum must she sit to have the seesaw balance?
Problem 6)
At one end of a lever is a 150 kg engine which is 2 meters from
the fulcrum. How much weight, in kg, should be placed on the other end 3 meters
from the fulcrum to balance?
3
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Problem 7)
A forklift places a lever under a 250 pound tank that is 8 feet from
the fulcrum. In order to lift the rock, how much force, in pounds, must the forklift
on the other end of the lever, if it is 10 feet from the fulcrum?
Problem 8)
Approximately where, in meters, should the fulcrum be placed
under a 15 meter lever if there is a 24 kg weight on one end and a 20 kg weight
on the other end in order to balance?
Problem 9) Randy weighs 217 pounds and sits 6 feet from the fulcrum of a
seesaw. If Joe weighs 186 pounds and sits on the other side, how far from the
fulcrum must he sit to have the seesaw balance?
4
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Problem 10)
At one end of a lever is a 40 kg weight which is 6 meters from
the fulcrum. How much weight should be placed on the other end 1.5 meters
from the fulcrum to balance?
Problem 11)
A person places a lever under a 18 pound cement block that is 3
feet from the fulcrum. In order to lift the rock, how much force, in pounds, must
the person on the other end of the lever, if he is 6 feet from the fulcrum?
Problem 12)
Approximately where, in meters, should the fulcrum be placed
under a 8 meter lever if there is a 48 kg weight on one end and a 64 kg weight on
the other end in order to balance?
5
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Problem 13) Leonard weighs 208 pounds and sits 7 feet from the fulcrum of a
seesaw. If Mark weighs 182 pounds and sits on the other side, how far, in feet,
from the fulcrum must he sit to have the seesaw balance?
Problem 14)
At one end of a lever is a 5.8 kg weight which is 2.4 meters from
the fulcrum. How much weight, in kg, should be placed on the other end 1.6
meters from the fulcrum to balance?
Problem 15)
A person places a lever under a 16.1 pound rock that is 4.8 feet
from the fulcrum. In order to lift the rock, how much force, in pounds, must the
person on the other end of the lever, if he is 5.6 feet from the fulcrum?
6
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Problem 16)
Approximately where, in meters, should the fulcrum be placed
under a 14 meter lever if there is a 9 kg weight on one end and a 6 kg weight on
the other end in order to balance?
Problem 17) Clarence weighs 154 pounds and sits 6 feet from the fulcrum of a
seesaw. If Kathy weighs 132 pounds and sits on the other side, how far, in feet,
from the fulcrum must she sit to have the seesaw balance?
Problem 18)
At one end of a lever is a 320 kg weight which is 5 meters from
the fulcrum. How much weight, in kg, should be placed on the other end 8 meters
from the fulcrum to balance?
7
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Problem 19)
A person places a lever under a 180 pound rock that is 12 feet
from the fulcrum. In order to lift the rock, how much force, in pounds must the
person on the other end of the lever, if he is 24 feet from the fulcrum?
Problem 20)
Where should, in meters, the fulcrum be placed under a 12
meter lever if there is a 10 kg weight on one end and a 8 kg weight on the other
end in order to balance?
8
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Answers - Algebra Word Problems – Lesson 9, Worksheet 9, Algebra Word
Problems Involving Levers
Problem 1) Jacob weighs 90 pounds and sits 6 feet from the fulcrum of a
seesaw. If Sally weighs 120 pounds and sits on the other side, how many feet
from the fulcrum must she sit to have the seesaw balance?
Solution:
The fulcrum is balanced with the formula 𝑙1 ∙ 𝑤1 = 𝑙2 ∙ 𝑤2.
Substitute the numbers from this problem:
90 ∙ 6 = 120 ∙ 𝑙
540 = 120 ∙ 𝑙
𝑙=
540
= 4.5
120
Answer: 4.5
Problem 2)
At one end of a lever is a 14 kg weight which is 9 meters from the
fulcrum. How much weight, in kg, should be placed on the other end 18 meters
from the fulcrum to balance?
Solution:
The fulcrum is balanced with the formula 𝑙1 ∙ 𝑤1 = 𝑙2 ∙ 𝑤2.
Substitute the numbers from this problem:
14 ∙ 9 = 𝑤 ∙ 18
126 = 18𝑤
𝑤=
126
=7
18
Answer: 7
9
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Problem 3)
A person places a lever under a 240 pound weight that is 6 feet
from the fulcrum. In order to lift the rock, how much force must the person on
the other end of the lever, if he is 9 feet from the fulcrum?
Solution:
The fulcrum is balanced with the formula 𝑙1 ∙ 𝑤1 = 𝑙2 ∙ 𝑤2.
Substitute the numbers from this problem:
240 ∙ 6 = 𝑤 ∙ 9
1440 = 9𝑤
𝑤=
1440
= 160
9
Answer: 160
Problem 4)
Where should the fulcrum, in feet, be placed under a 12 meter
lever if there is a 24 kg weight on one end and a 36 kg weight on the other end in
order to balance?
Solution:
The fulcrum is balanced with the formula 𝑙1 ∙ 𝑤1 = 𝑙2 ∙ 𝑤2.
Substitute the numbers from this problem:
𝑙 ∙ 24 = (12 − 𝑙) ∙ 36
24𝑙 = 432 − 36𝑙
48𝑙 = 432
𝑙=
432
=9
48
Answer: 9
10
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Problem 5) Brian weighs 56 kg and sits 1.8 meters from the fulcrum of a
seesaw. If Lisa weighs 48 kg and sits on the other side, how far, in meters, from
the fulcrum must she sit to have the seesaw balance?
Solution:
The fulcrum is balanced with the formula 𝑙1 ∙ 𝑤1 = 𝑙2 ∙ 𝑤2.
Substitute the numbers from this problem:
1.8 ∙ 56 = 48 ∙ 𝑙
100.8 = 48𝑙
𝑙=
100.8
= 2.1
48
Answer: 2.1
Problem 6)
At one end of a lever is a 150 kg engine which is 2 meters from
the fulcrum. How much weight, in kg, should be placed on the other end 3 meters
from the fulcrum to balance?
Solution:
The fulcrum is balanced with the formula 𝑙1 ∙ 𝑤1 = 𝑙2 ∙ 𝑤2.
Substitute the numbers from this problem:
150 ∙ 2 = 𝑤 ∙ 3
300 = 3𝑤
𝑤=
300
= 100
3
Answer: 100
11
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Problem 7)
A forklift places a lever under a 250 pound tank that is 8 feet from
the fulcrum. In order to lift the rock, how much force, in pounds, must the forklift
on the other end of the lever, if it is 10 feet from the fulcrum?
Solution:
The fulcrum is balanced with the formula 𝑙1 ∙ 𝑤1 = 𝑙2 ∙ 𝑤2.
Substitute the numbers from this problem:
250 ∙ 8 = 𝑤 ∙ 10
2000 = 10𝑤
𝑤=
2000
= 200
10
Answer: 200
Problem 8)
Approximately where, in meters to the nearest tenth, should the
fulcrum be placed under a 15 meter lever if there is a 24 kg weight on one end
and a 20 kg weight on the other end in order to balance?
Solution:
The fulcrum is balanced with the formula 𝑙1 ∙ 𝑤1 = 𝑙2 ∙ 𝑤2.
Substitute the numbers from this problem:
𝑙 ∙ 24 = (15 − 𝑙) ∙ 20
24𝑙 = 300 − 20𝑙
44𝑙 = 300
𝑙=
300
= 6.8
44
Answer: 6.8
12
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Problem 9) Randy weighs 217 pounds and sits 6 feet from the fulcrum of a
seesaw. If Joe weighs 186 pounds and sits on the other side, how far from the
fulcrum must he sit to have the seesaw balance?
Solution:
The fulcrum is balanced with the formula 𝑙1 ∙ 𝑤1 = 𝑙2 ∙ 𝑤2.
Substitute the numbers from this problem:
217 ∙ 6 = 𝑙 ∙ 186
1302 = 186𝑙
𝑙=
1302
=7
186
Answer: 7
Problem 10)
At one end of a lever is a 40 kg weight which is 6 meters from
the fulcrum. How much weight should be placed on the other end 1.5 meters
from the fulcrum to balance?
Solution:
The fulcrum is balanced with the formula 𝑙1 ∙ 𝑤1 = 𝑙2 ∙ 𝑤2.
Substitute the numbers from this problem:
40 ∙ 6 = 1.5 ∙ 𝑤
240 = 1.5𝑤
𝑤=
240
= 160
1.5
Answer: 160
13
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Problem 11)
A person places a lever under a 18 pound cement block that is 3
feet from the fulcrum. In order to lift the rock, how much force, in pounds, must
the person on the other end of the lever, if he is 6 feet from the fulcrum?
Solution:
The fulcrum is balanced with the formula 𝑙1 ∙ 𝑤1 = 𝑙2 ∙ 𝑤2.
Substitute the numbers from this problem:
18 ∙ 3 = 6 ∙ 𝑤
54 = 6𝑤
𝑤=
54
=9
6
Answer: 9
Problem 12)
Approximately where, in meters to the nearest tenth, should the
fulcrum be placed under a 8 meter lever if there is a 48 kg weight on one end and
a 64 kg weight on the other end in order to balance?
Solution:
The fulcrum is balanced with the formula 𝑙1 ∙ 𝑤1 = 𝑙2 ∙ 𝑤2.
Substitute the numbers from this problem:
𝑙 ∙ 48 = (8 − 𝑙)64
48𝑙 = 512 − 64𝑙
112𝑙 = 512
𝑙=
512
= 4.571428~4.6
112
Answer: 4.6
14
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Problem 13) Leonard weighs 208 pounds and sits 7 feet from the fulcrum of a
seesaw. If Mark weighs 182 pounds and sits on the other side, how far, in feet,
from the fulcrum must he sit to have the seesaw balance?
Solution:
The fulcrum is balanced with the formula 𝑙1 ∙ 𝑤1 = 𝑙2 ∙ 𝑤2.
Substitute the numbers from this problem:
208 ∙ 7 = 𝑙 ∙ 182
1456 = 182𝑙
𝑙=
1456
=8
182
Answer: 8
Problem 14)
At one end of a lever is a 5.8 kg weight which is 2.4 meters from
the fulcrum. How much weight, in kg, should be placed on the other end 1.6
meters from the fulcrum to balance?
Solution:
The fulcrum is balanced with the formula 𝑙1 ∙ 𝑤1 = 𝑙2 ∙ 𝑤2.
Substitute the numbers from this problem:
2.4 ∙ 5.8 = 𝑙 ∙ 1.6
13.92 = 1.6𝑙
𝑙=
13.92
= 8.7
1.6
Answer: 8.7
15
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Problem 15)
A person places a lever under a 16.1 pound rock that is 4.8 feet
from the fulcrum. In order to lift the rock, how much force, in pounds to the
nearest tenth, must the person on the other end of the lever, if he is 5.6 feet from
the fulcrum?
Solution:
The fulcrum is balanced with the formula 𝑙1 ∙ 𝑤1 = 𝑙2 ∙ 𝑤2.
Substitute the numbers from this problem:
16.1 ∙ 4.8 = 5.6 ∙ 𝑤
77.28 = 5.6𝑤
𝑤=
77.28
= 13.8
5.6
Answer: 13.8
Problem 16)
Approximately where, in meters to the nearest tenth, should the
fulcrum be placed under a 14 meter lever if there is a 9 kg weight on one end and
a 6 kg weight on the other end in order to balance?
Solution:
The fulcrum is balanced with the formula 𝑙1 ∙ 𝑤1 = 𝑙2 ∙ 𝑤2.
Substitute the numbers from this problem:
𝑙 ∙ 9 = (14 − 𝑙) ∙ 6
9𝑙 = 84 − 6𝑙
15𝑙 = 84
𝑙=
84
= 5.6
15
Answer: 5.6
16
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Problem 17) Clarence weighs 154 pounds and sits 6 feet from the fulcrum of a
seesaw. If Kathy weighs 132 pounds and sits on the other side, how far, in feet,
from the fulcrum must she sit to have the seesaw balance?
Solution:
The fulcrum is balanced with the formula 𝑙1 ∙ 𝑤1 = 𝑙2 ∙ 𝑤2.
Substitute the numbers from this problem:
154 ∙ 6 = 𝑙 ∙ 132
924 = 132𝑙
𝑙=
924
=7
132
Answer: 7
Problem 18)
At one end of a lever is a 320 kg weight which is 5 meters from
the fulcrum. How much weight, in kg, should be placed on the other end 8 meters
from the fulcrum to balance?
Solution:
The fulcrum is balanced with the formula 𝑙1 ∙ 𝑤1 = 𝑙2 ∙ 𝑤2.
Substitute the numbers from this problem:
320 ∙ 5 = 8 ∙ 𝑤
1600 = 8𝑤
𝑤=
1600
= 200
8
Answer: 200
17
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Problem 19)
A person places a lever under a 180 pound rock that is 12 feet
from the fulcrum. In order to lift the rock, how much force, in pounds must the
person on the other end of the lever, if he is 24 feet from the fulcrum?
Solution:
The fulcrum is balanced with the formula 𝑙1 ∙ 𝑤1 = 𝑙2 ∙ 𝑤2.
Substitute the numbers from this problem:
180 ∙ 12 = 24 ∙ 𝑤
2160 = 24𝑤
𝑤=
2160
= 90
24
Answer: 90
Problem 20)
Where should, in meters, the fulcrum be placed under a 12
meter lever if there is a 10 kg weight on one end and a 8 kg weight on the other
end in order to balance?
Solution:
The fulcrum is balanced with the formula 𝑙1 ∙ 𝑤1 = 𝑙2 𝑤2.
Substitute the numbers from this problem:
10 ∙ 𝑙 = (12 − 𝑙)8
10𝑙 = 96 − 8𝑙
18𝑙 = 96
𝑙=
Answer: 5
96
1
=5
18
3
1
3
18
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