FIND MISSING QUANTITIES IN PROPORTION

Solve for the unknown.

Problem 1 :

3 : n = 5 : 20

Solution:

3 : n = 5 : 20

If two ratios are equal, then

Product of means = Product of extremes

3 ⋅ 20 = n ⋅ 5

60 = 5n

n = 12

Problem 2 :

a : 42 = 5 : 6

Solution:

a : 42 = 5 : 6

If two ratios are equal, then

Product of means = Product of extremes

a ⋅ 6 = 42 ⋅ 5

6a = 210

a = 35

Problem 3 :

50 : 75 = x : 1/2

Solution:

50 : 75 = x : 1/2

If two ratios are equal, then

Product of means = Product of extremes

50 ⋅ 1/2 = 75 ⋅ x

25 = 75x

x = 25/75

x = 1/3

Problem 4 :

7 : 3.5 = 21 : z

Solution:

7 : 3.5 = 21 : z

If two ratios are equal, then

Product of means = Product of extremes

7 ⋅ z = 3.5 ⋅ 21

7z = 73.5

z = 73.5/7

z = 10.5

Problem 5 :

0.6 : g = 0.78 : 0.325

Solution:

0.6 : g = 0.78 : 0.325

If two ratios are equal, then

Product of means = Product of extremes

0.6 ⋅ 0.325 = g ⋅ 0.78

0.195 = 0.78g

g = 0.195/0.78

g = 0.25

Problem 6 :

7/8 : 3/16 = t : 5/8

Solution:

7/8 : 3/16 = t : 5/8

If two ratios are equal, then

Product of means = Product of extremes

Use proportions to solve the following problems.

Problem 7 :

A box of 500 vitamin C tablets sells for $4.80. How much would 125 tablets cost?

Solution:

Let n be the missing part.

tablets : price

500 : 4.80 = 125 : n

Product of means = Product of extremes

500 : 4.80 = 125 : n

500 n = 600

n = 600/500

n = $1.2

Problem 8 :

If you can open 12 cans of soup in 5 minutes, how many cans of soup could you open in 45 minutes?

Solution:

Let n be the missing part.

cans : minutes

12 : 5 = n : 45

Product of means = Product of extremes

12 : 5 = n : 45

5n = 540

n = 540/5

n = 108 cans of soup

Problem 9 :

A manufacturing plant can make 750 microwave ovens in 9 days. How large an order for microwave ovens can the plant fill in 33 days?

Solution:

Let n be the missing part.

microwave ovens : days

750 : 9 = n : 33

Product of means = Product of extremes

750 : 9 = n : 33

9n = 24750

n = 24750/9

n = 2750 microwave ovens

Problem 10 :

R. Habsburg has a three-fifths interest in a salt mining operation. He sold five-sevenths of his interest for $4,500. (a) What was the total amount of Habsburg's interest in the operation before selling? (b) What is the total value of the salt mining operation?

Solution:

(a)

4500 is 5/7 of his interest, which we can let x.

b) 6300 was 3/5 of the total value of the operation, which we can let x.