# FIND THE MISSING TERM IN PROPORTION

proportion is a statement that two quantities are equal. If two ratios are equal, then they will be in proportion.

a : b = c : d

a d = bc (Product of means = Product of extremes)

Find the missing term in each proportion.

Problem 1 :

1/2 = ?/8

Solution :

1/2 = ?/8

1 × 8 = 2 × x

8 = 2x

x = 8/2

x = 4

Problem 2 :

3/5 = 18/?

Solution :

3/5 = 18/?

3x = 5 × 18

3x = 90

x = 90/3

x = 30

Problem 3 :

1/4 = 6/?

Solution :

1/4 = 6/?

x = 4 × 6

x = 24

Problem 4 :

4/6 = ?/42

Solution :

4/6 = ?/42

4 × 42 = 6 × x

168 = 6x

x = 168/6

x = 28

Problem 5 :

4 : ? = 12 : 60

Solution :

4 : ? = 12: 60

4 × 60 = x × 12

240 = 12x

x = 240/12

x = 20

Problem 6 :

? : 9 = 35 : 63

Solution :

? : 9 = 35 : 63

x × 63 = 9 × 35

63x = 315

x = 315/63

x = 5

Problem 7 :

? : 60 = 6 : 10

Solution :

? : 60 = 6 : 10

x × 10 = 60 × 6

10x = 360

x = 360/10

x = 36

Problem 8 :

16 : ? = 12 : 9

Solution :

16 : ? = 12 : 9

16 × 9 = x × 12

144 = 12x

x = 144/12

x = 12

Solve each equation and check the solution.

Problem 9 :

x/60 = 3/20

Solution :

x/60 = 3/20

20 × x = 3 × 60

20x = 180

x = 180/20

x = 9

To check:

9/60 = 3/20

By cross multiplying,

9 × 20 = 3 × 60

180 = 180

Problem 10 :

5/4 = x/12

Solution :

5/4 = x/12

5 × 12 = 4 × x

60 = 4x

x = 60/4

x = 15

To check:

5/4 = 15/12

By cross multiplying,

5 × 12 = 4 × 15

60 = 60

Problem 11 :

30/4x = 10/24

Solution :

30/4x = 10/24

30 × 24 = 10 × 4x

720 = 40x

x = 720/40

x = 18

To check:

30/4(18) = 10/24

30/72 = 10/24

By cross multiplying,

30 × 24 = 10 × 72

720 = 720

Problem 12 :

5/15 = x/(x + 8)

Solution :

5/15 = x/(x + 8)

5(x + 8) = 15 × x

5x + 40 = 15x

40 = 10x

x = 40/10

x = 4

To check:

5/15 = 4/(4 + 8)

5/15 = 4/12

By cross multiplying,

5 × 12 = 15 × 4

60 = 60

Problem 13 :

x/(12 - x) = 10/30

Solution :

x/(12 - x) = 10/30

x × 30 = 10 × (12 - x)

30x = 120 - 10x

30x + 10x = 120

40x = 120

x = 120/40

x = 3

To check:

3/(12 - 3) = 10/30

3/9 = 10/30

By cross multiplying,

3 × 30 = 9 × 10

90 = 90

Problem 14 :

16/8 = (21 - x)/x

Solution :

16/8 = (21 - x)/x

16 × x = 8 × (21 - x)

16x = 168 - 8x

16x + 8x = 168

24x = 168

x = 168/24

x = 7

To check:

16/8 = (21 - 7)/7

16/8 = 14/7

By cross multiplying,

16 × 7 = 8 × 14

112 = 112

Problem 15 :

(3x + 3)/3 = (7x - 1)/5

Solution :

(3x + 3)/3 = (7x - 1)/5

5 × (3x + 3) = 3 × (7x - 1)

15x + 15 = 21x - 3

15x - 21x = -15 - 3

-6x = -18

x = -18/-6

x = 3

To check:

(3(3) + 3)/3 = (7(3) - 1)/5

12/3 = 20/5

By cross multiplying,

12 × 5 = 3 × 20

60 = 60

Problem 16 :

12 : 15 = x : 45

Solution :

12 : 15 = x : 45

12 × 45 = 15 × x

540 = 15x

x = 540/15

x = 36

To check:

12: 15 = 36: 45

12(45) = 15(36)

540 = 540

Problem 17 :

5: x + 2 = 4: x

Solution :

5: x + 2 = 4: x

5x = 4(x + 2)

5x = 4x + 8

x = 8

To check:

5: 10 = 4: 8

5(8) = 10(4)

40 = 40

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