1. 3-6 Solve Proportions Using Cross Products

2. Vocabulary Cross Product:
The product of the numerator of one ratio and the denominator of a second ratio.
The cross products of a proportion are equal.
Example: 3 = 6
3 (8) = 6 (4)
= 24

3. Example 1 4 (24) = 12(2x) 96 = 24x 24 24 x = 4 Solve the proportion:
4 = 2x
Cross Multiply.
4 (24) = 12(2x)
Solve the Equation.
96 = 24x 24 24
x = 4

4. Example 2 3(x - 4) = 9x 3x – 12 = 9x -3x -3x -12 = 6x 6 6 x = -2
What is the value of x in the proportion?
Put ( ) around the expression part first
3 =
x x-4
( )
Cross Multiply.
3(x - 4) = 9x
Simplify by Distributing.
3x – 12 = 9x
Solve for x.
-3x x
Subtract 3x from both sides.
Divide both sides by 6.
-12 = 6x
x = -2

5. Example 3 = peat moss perlite 4 3 10 x x = 7.5 buckets of perlite
Georgia is making her own potting soil. For every 4 buckets of peat moss, she mixes in 3 buckets of perlite. If she uses 10 buckets of peat moss, how many buckets of perlite should she use? Write and solve a proportion to find the answer.
peat moss
perlite 4 3 10 x =
4x = 30
Cross Multiply.
Solve:
Divide both sides by 4.
x = 7.5 buckets of perlite

6. Homework
Section 3-6
Page
4 - 10,
24 – 27

7. 3-7 Solve Percent Problems

8. Vocabulary Percent: Means “divided by 100”.
“a is p percent of b” using a proportion:
a = p b
In General for 3.7:

9. Example 1
Find a percent using a proportion.
What percent of 60 is 9? IS OF %
100 = 9 60 p
100
9(100) = 60p =
900 = 60p
p = 15%

10. Example 2
Find a percent using a proportion.
13 is what percent of 20? IS OF %
100 = 13 20 p
100
13(100) = 20p =
1300 = 20p
p = 65%

11. Example 3 = = What number is 12% of 85? IS OF % 100 x 85 12 100
x = 10.2

12. Example 4 75 is 62.5% of what number? = = IS OF % 100 75 x 62.5 100
x = 120

13. Homework
Section 3-7
Page 179 – 181
3 – 18 all,
26 – 29 all,
33, 34