1. Ch 8: Exponents G) Mixture Word Problems
Objective:
To solve mixture word problems.

2. Illustration + = 10 oz 6 oz 4 oz 25% solution 50% solution
1/4
3/6
4/10

3. Rules 1) Set up a table (see below) and insert given data Total Size %
Item A × + +
Item B ×
Mixture ×
2) Multiply across to determine the Total for each row
3) Add down to calculate the Mixture row
4) Solve the equation from the Mixture row

4. Example 1
9 oz. of mixed nuts containing 40% peanuts were mixed with 6 oz. of another kind of mixed nuts that contain 65% peanuts.
Peanuts are what percent of the new mixture?
Total
Size %
Mixed Nuts 1
9 oz ×
.40
3.60 + +
Mixed Nuts 2
6 oz
.65
3.90 ×
Mixture
15 oz x
7.5 oz 15 x =
7.5 15 15
x = .50
= 50%

5. Classwork 1
4 yd3 of soil containing 15% sand was mixed into 6 yd3 of soil containing 50% sand. What is the sand content of the mixture?
Total
Size %
Solution 1
4 yd3 ×
.15
.60 + +
Solution 2
6 yd3
.50
3.00 ×
Mixture
10 yd3 x
3.60 10 x =
3.6 10 10
x = .36
= 36%

6. Example 2
9 lb of Abhasra's special coffee blend was made by combining 3 lb of brand X coffee which costs $24/lb with 6 lb of brand Y coffee which costs $18/lb. Find the cost per lb of the mixture.
Total
Size
Cost
Brand X
3 lb ×
$24/lb
$72 + +
Brand Y
6 lb
$18/lb
$108 ×
Mixture
9 lb x
$180 9 x =
180 9 9
x = $20/lb

7. Classwork 2
Matt mixed together 2 liters of Brand A fruit punch and 3 liters of Brand B. Brand A contains 25% fruit juice and Brand B contains 30% fruit juice. What percent of the mixture is fruit juice?
Total
Size %
Brand A
2 L ×
.25
.50 + +
Brand B
3 L
.30
.90 ×
Mixture
5 L x
1.40 5 x =
1.4 5 5
x = .28
= 28%

8. Classwork 3
12 L of a 70% alcohol solution was mixed with 6 L of a 10% alcohol solution. What is the concentration of the mixture?
Total
Size %
Solution 1
12 L ×
.70
8.40 + +
Solution 2
6 L
.10
.60 ×
Mixture
18 L x
9.00 18 x = 9 18 18
x = .50
= 50%

9. Example 3
How many ml of an 88% alcohol solution must be mixed with 10 ml of pure water to make an 8% solution?
Total
Size %
Alcohol x ×
.88
.88x + +
Water
10 ml ×
Mixture
10 + x
.08
.88x
(10 + x)
(.08) =
.88x 8 =
.8x x =
.88x .8 .8
-.08x
-.08x
x = 10 ml

10. Classwork 4
How much of Brand A fruit punch (25% fruit juice) must be mixed with 10 gal. of Brand B fruit punch (55% fruit juice) to create a mixture containing 40% fruit juice?
Total
Size %
Brand A x ×
.25
.25x + +
Brand B
10 gal
.55
5.5 ×
Mixture
10 + x
.40 x
(10 + x)
(.40) = x
.15x =
1.5 x = x
.15
.15 -4
-.25x -4
-.25x
x = 10 gal

11. Classwork 5
How many lb of soybean oil which costs $4/lb must be added to 10 lb of canola oil which costs $1/lb to make vegetable oil which costs $2/lb?
Total
Size
Cost
Soybean Oil x ×
$4/lb 4x + +
Canola Oil
10 lb
$1/lb 10 ×
Mixture
10 + x
$2/lb
10 + 4x
(10 + x)
(2) =
10 + 4x 10 = 2x
20 + 2x =
10 + 4x 2 2
-10
-2x
-10
-2x
x = 5 lb

12. Classwork 6
Kayla created a metal containing 25% iron by combining two other metals. One of these metals weighed 1 mg and contained 70% iron. The other weighed 3 mg. How much iron did it contain?
Total
Size %
Metal 1
1 mg ×
.70 .7 + +
Metal 2
3 mg x 3x ×
Mixture
4 mg
.25
.7 + 3x
(4)
(.25) =
.7 + 3x .3 = 3x
1.00 =
.7 + 3x 3 3
-.7
-.7
x = .10
= 10%