Solved Examples and Worksheet for Applications of Linear Equations
Q1
A number divided by negative 3 is equal to 7.
What is the number?
A
. - 19
B
. - 23
C
. 21
D
. - 21
Solutions
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Step: 1
Let
n
be the unknown number.
[Identify the variable.]
Step: 2
n
-
3
= 7
[Write the phrase as an equation.]
Step: 3
n
-
3
× - 3 = 7 × - 3
[Multiply each side by - 3.]
Step: 4
n
= - 21
[Simplify.]
Step: 5
The unknown number is - 21.
Correct Answer is :
- 21
Q2
The difference between a number and
3
7
is 48. What is the number?
A
.
48
3
7
B
.
50
3
7
C
.
47
3
7
D
.
49
3
7
Solutions
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Step: 1
Let
k
be the unknown number.
Step: 2
k
-
3
7
= 48
[Write the equation.]
Step: 3
k
-
3
7
+
3
7
= 48 +
3
7
[Add
3
7
on each side.]
Step: 4
k
=
339
7
[Simplify.]
Step: 5
k
=
48
3
7
[Convert improper fraction into mixed number.]
Step: 6
The number is
48
3
7
.
Correct Answer is :
48
3
7
Q3
What is the number, if one seventh of the number is 48?
A
. 6
B
. 7
C
. 336
D
. 337
Solutions
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Step: 1
Let
p
be the number.
Step: 2
p
×
1
7
= 48
[Original equation.]
Step: 3
p
7
× 7 = 48 × 7
[Multiply each side by 7.]
Step: 4
p
= 336
[Simplify.]
Step: 5
The number is 336.
Correct Answer is :
336
Q4
A number divided by 3 equals 15.
What is the number?
A
. 15
B
. 45
C
. 18
D
. None of the above
Solutions
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Step: 1
Let
n
be the number.
Step: 2
n
3
= 15
[Original equation.]
Step: 3
n
3
× 3 = 15 × 3
[Multiply each side with 3.]
Step: 4
n
= 45
[Simplify.]
Step: 5
The number is 45.
Correct Answer is :
45
Q5
The sum of 31 and another number is 39. What is the number?
A
. 7
B
. 10
C
. 8
D
. 9
Solutions
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Step: 1
Let
a
be the another number.
Step: 2
31 +
a
= 39
[Original equation.]
Step: 3
31 +
a
- 31 = 39 - 31
[Subtract 31 from each side.]
Step: 4
a
= 8
[Simplify.]
Step: 5
The other number is 8.
Correct Answer is :
8
Q6
If the sum of
2
5
and a number is equal to
1
2
, then what is the number?
A
.
1
11
B
.
1
10
C
. 1
D
.
1
5
Solutions
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Step: 1
Let
n
be the number.
Step: 2
2
5
+
n
=
1
2
[Write an eqaution.]
Step: 3
n
+
2
5
-
2
5
=
1
2
-
2
5
[Subtract
2
5
from both sides.]
Step: 4
=
5
-
4
1
0
Step: 5
n
=
1
10
[Simplify.]
Step: 6
So, the number is
1
10
.
Correct Answer is :
1
10
Q7
If a number is subtracted from
7
3
, the result is
11
5
. Find the number.
A
.
3
16
B
.
2
15
C
.
1
5
D
.
4
15
Solutions
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Step: 1
Let
x
be the number.
Step: 2
7
3
-
x
=
11
5
[Write an equation.]
Step: 3
7
3
-
x
-
7
3
=
11
5
-
7
3
[Subtract
7
3
from each side.]
Step: 4
-
x
=
33-35
15
[LCD of 5, 3 is 15.]
Step: 5
-
x
= -
2
15
[Subtract 35 from 33.]
Step: 6
x
=
2
15
[Multiply each side by -1.]
Step: 7
The number is
2
15
.
Correct Answer is :
2
15
Q8
The difference between a number and
3
7
is 30. What is the number?
A
. 70
B
.
30
3
7
C
.
29
4
7
D
.
90
7
Solutions
Share
Step: 1
Let
k
be the unknown number.
Step: 2
k
-
3
7
= 30
[Write the equation.]
Step: 3
k
-
3
7
+
3
7
= 30 +
3
7
[Add
3
7
on each side.]
Step: 4
k
=
213
7
[Simplify.]
Step: 5
k
=
30
3
7
[Convert improper fraction into mixed number.]
Step: 6
The number is
30
3
7
.
Correct Answer is :
30
3
7
Q9
If the sum of
3
7
and a number is equal to
2
3
, then what is the number?
A
.
5
21
B
. 5
C
.
2
7
D
.
5
22
Solutions
Share
Step: 1
Let
n
be the number.
Step: 2
3
7
+
n
=
2
3
[Write an eqaution.]
Step: 3
n
+
3
7
-
3
7
=
2
3
-
3
7
[Subtract
3
7
from both sides.]
Step: 4
=
14-9
21
Step: 5
n
=
5
21
[Simplify.]
Step: 6
So, the number is
5
21
.
Correct Answer is :
5
21
Q10
The sum of 25 and another number is 32. What is the number?
A
. 32
B
. 7
C
. 6
D
. 57
Solutions
Share
Step: 1
Let
a
be the another number.
Step: 2
25 +
a
= 32
[Original equation.]
Step: 3
25 +
a
- 25 = 32 - 25
[Subtract 25 from each side.]
Step: 4
a
= 7
[Simplify.]
Step: 5
The other number is 7.
Correct Answer is :
7
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Related Topic
Linear Equation
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