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.
May 21, 24 08:51 PM
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