Proportions and Percents
Proportions:
A proportion is a statement that two ratios are equal. When trying to solve proportions we use the Cross Products Property of Proportions.
A=C A(D) = B(C)
B D
Example:
6__ =x__ x + 5__ =1.5___
11 121 12 6
6(121) = 11x 6(x + 5) = 12(1.5)
726 = 11x 6x + 30 = 18
-30 -30
726 =11x6x =-12
11 11 6 6
66 = x x = -2
1) x _ = 16 2) x – 3 _ = 12 _
14 35 x + 3 30
Percents:
Is=%___
Of 100
Example:
What number is 20% of 50?
Is: ? x x=20 .
Of: of 50 50 100
%: 20%
100: 100 100x = 20(50)
100x = 1,000
100x =1,000
100 100
x = 10
a) What number is 40% of 160? b) 48 is what percent of 128?
c) 28 is 75% of what number?d) What number is 36% of 400?
Part I:
1)x . =18 . 2) 5 . =65 . 3) x + 4 . =6x .
12 54 x 90 9 18
4) -16 . =8 .5)14. =3x .
6x-2 11 16 3x + 3
6) What is 20% of 32? 7) 72 is 40% of what number?
8) 21.56 is what percent of 98? 9) - 31 is what percent of -124?
10) What is 62% of 140?
Part II:
1)x . =13 . 2) -13 . =195 . 3) x + 4 . =6x .
12 78 x 150 9 18
4) -16 . =4 . 5)x + 5 . =x . 6) x-4 _ = 9 _
6x - 4 13 x - 3 9 12 x+8
7) 12 is 40% of what number?
8) 37.24 is what percent of 98? 9) 45 is what percent of 180?
10) What is 62% of 70?
Part III:
1)23 . =57.5 . 2) 3x – 5 . =5x + 1 . 3) 5x -1=33 .
x 45 13 52 10x+5 45
4)x + 1 . = 2 . 5) 2x – 4 . =x - 2 . 6) x + 7 = x + 14.
x + 6 x x + 5x + 1 2x – 1 x - 2
7) What is 80% of 850?8) 128 is 32% of what number?
9) 72 is what percent of 120?10) What is 80% of 850?
Proportion Practice
1) 7 _ = x _2) x _ = 39 _
12 66 33 107.25
3) x _ = 3 _4) x + 11 _ = -1 _
x + 4 5 x - 53
5) 14 _ = 7 _6) 6x - 3 _ = 6 _
5x - 1 2x + 2 11x + 20 14
7) 3 _ = 2x - 1 _8) 2x - 5 _ = 4x - 14 _
8 7x + 4 1520
9) x _ = 6 _10) x + 2 _ = 2 _
4 x + 2 15 x + 3
11) 6 _ = x + 5 _12) x _ = x + 4 _
x - 2 5 2x + 1 x + 14
13) x - 2 _ = x + 2 _14) x + 4 _ = 2x - 3 _
x + 2 2x + 4 x + 8 x – 6
15) x + 2 _ = x - 6 _16) x + 3 _ = x + 10 _
x + 5 x - 5 2x + 6x + 7
17) 2x + 5 _ = x + 4 _18) 2x - 3 _ = x + 6 _
x + 10 x + 8 xx + 4
19) x - 6 _ = x - 3 _20) 2x - 6 _ = 3x -5 _
x + 6 x + 5 x + 6 x + 5
Answer Key to pg. 3:
1) 38.52) 12
3) 64) -7
5) 56) 9
7) -48) 5.5
9) x = {-6,4}10) x = {-8,3}
11) x = {-8,5}12) x = {1,4}
13) x = {-2,6}14) x = {-15,0}
15) 1016) x = {-13,-3}
17) x = {-7,0}18) x = {-3,4}
19) -320) x = {-9,0}
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