A 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
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM