Mixture Problems

Mixture Problems This lesson must be completed with the mixture handout

Partner Brainstorm • If you mix 50 apples and 25 peaches in a basket, what part of the basket mixture is apples? • What percent of the basket mixture is peaches? 50 apples out of a total of 75 fruits 25 apples out of a total of 75 fruits 25 = x % = 33% 75 100

Solve problems that use“is over of equals percent over 100” • If a mixture of 10 items is 60% nails, how many nails are in the mixture? • If a mixture of 60 items is 40% pencils, how many pencils are in the mixture?

Handout Problem 1Mixing Chemicals • Suppose you work in a lab. You need a 50% acid solution for a lab test, but your supplier only ships a 40% solution and a 70% solution. Rather than pay extra fees you decide to mix the acids yourself. You are using 50 liters of the 40% solution. How many liters of a 70% acid solution do you need to get 50% acid? • STEP 1: Set up table

How many liters of a 70% acid solution must be added to 50 liters of a 40% acid solution to produce a 50% acid solution? STEP 1: Set up and fill in table with information then multiply across the table X 0.70 0.70x 50 0.40 (50)(0.40)=20 50+x0.50 (50+x)(0.50)

STEP 2: Add up last column and write an equation 0.7x + 20 = 0.5(50+x) Solve for x and compare answers

Handout Problem 2Mixing Water How many ounces of pure watermust be added to 50 ounces of a 15% salt solution to make a salt solution that is 10% salt? STEP 1: Set up and fill table X 0 0x = 0 50 0.15 (50)(0.15)=7.5 50+x0.10 (50+x)(0.10)

STEP 2: Add up last column and write an equation X 0 0x = 0 50 0.15 (50)(0.15)=7.5 50+x0.10 (50+x)(0.10) 0 + 7.5 = 0.1(50+x) Solve for x and compare answers

Handout Problem 3Coffee Mixture Find the selling price per pound of a coffee mixture made from 8 pounds of coffee that sells for $9.20 per pound and 12 pounds of coffee that costs $5.50 per pound STEP 1: Set up and fill table • $9.20 (8)($9.20) • =$73.60 12 $5.50(12)($5.50) =$66 8+12=20 ? Add em=139.60

$9.20 (8)($9.20) • =$73.60 From the last row, you see that you have 20 pounds for $139.60 or $139.60/(20 pounds). Simplify 12 $5.50(12)($5.50) =$66 8+12=20 ? Add em=139.60

Handout Problem 4Veggies How many pounds of lima beans that cost $0.90 per pound must be mixed with 16 lbs of corn that costs $0.50 per pound to make a mixture of vegetables that costs $0.65 per pound? STEP 1: Set up and fill table x $0.90 (x)($0.90) 16 $0.50(16)($0.50) =$8 16+x $0.65 (16+x)($0.65)

x $0.90 (x)($0.90) $0.90x + $8 = (16+x)($0.65) Solve for x 16 $0.50(16)($0.50) =$8 16+x $0.65 (16+x)($0.65) STEP 2: Add up last column and write an equation

Handout Problem 5Fruit Drinks Two hundred liters of a punch that contains 35% fruit juice is mixed with 300 liters (L) of another punch. The resulting fruit punch is 20% fruit juice. Find the percent of fruit juice in the 300 liters of punch STEP 1: Set up and fill table • 0.35 (200)(0.35) • =70 300 x(300)(x) 200+300=500 0.20 (500)(0.20) =100

0.35 (200)(0.35) • =70 70 +300x = 100 Solve for x, and then convert to a percent 300 x(300)(x) 200+300=500 0.20 (500)(0.20) =100 STEP 2: Add up last column and write an equation

Handout Problem 6Breakfast Cereal Ten grams of sugar are added to a 40 gram serving of a breakfast cereal that is 30% sugar. What is the percent concentration of sugar in the resulting mixture? STEP 1: Set up and fill table 40 0.30 (40)(0.30)=12 10 1.00(10)(1)=10 (100%sugar) 50 ? 10+12=22

40 0.30 (40)(0.30)=12 22 grams of sugar in the 50 gram bowl so 22/50 simplify and then convert to a percentage 10 1.00(10)(1)=10 (100%sugar) 50 ? 10+12=22

Mixture Problems