SOLVING PROPORTIONS WITH VARIABLES

Solve each Proportion :

Problem 1 :

2/r = 12/18

Solution :

2/r = 12/18

By using cross multiplication, we get

2 × 18 = 12 × r

36 = 12r

Dividing both parts by 12, we get

36/12 = r

r = 3

Problem 2 :

50/20 = 5/h

Solution :

50/20 = 5/h

By using cross multiplication, we get

50 × h = 5 × 20

50h = 100

Dividing both parts by 50, we get

h = 100/50

h = 2

Problem 3 :

16/6 = 3d/9

Solution :

16/6 = 3d/9

By using cross multiplication, we get

16 × 9 = 3d × 6

144 = 18d

Dividing both parts by 18, we get

144/18 = d

 d = 8

Problem 4 :

45/27 = x/3

Solution :

45/27 = x/3

By using cross multiplication, we get

45 × 3 = x × 27

135 = 27x

Dividing both parts by 27, we get

135/27 = x

x = 5

Problem 5 :

v/84 = 2/21

Solution :

v/84 = 2/21

By using cross multiplication, we get

v × 21 = 2 × 84

21v = 168

Dividing both parts by 21, we get

v = 168/21

v = 8

Problem 6 :

b/8 = 8/64

Solution :

b/8 = 8/64

By using cross multiplication, we get

b × 64 = 8 × 8

64b = 64

Dividing both parts by 64, we get

b = 64/64

b = 1

Problem 7 :

13/3 = 26/c

Solution :

13/3 = 26/c

By using cross multiplication, we get

13 × c = 26 × 3

13c = 78

Dividing both parts by 13, we get

c = 78/13

c = 6

Problem 8 :

27/15 = 72/a

Solution :

27/15 = 72/a

By using cross multiplication, we get

27 × a = 72 × 15

27a = 1680

Dividing both parts by 27, we get

a = 1680/27

a = 40

Problem 9 :

15/n = 5/12

Solution :

15/n = 5/12

By using cross multiplication, we get

15 × 12 = 5 × n

180 = 5n

Dividing both parts by 5, we get

180/5 = n

n = 36

Problem 10 :

20/8 = 4k/32

Solution :

20/8 = 4k/32

By using cross multiplication, we get

20 × 32 = 4k × 8

640 = 32k

Dividing both parts by 32, we get

640/32 = k

k = 20