# Mixture Problems

Video solutions to help Grade 7 students write and use algebraic expressions and equations to solve percent word problems related to mixtures.

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Lesson Plans and Worksheets for Grade 7

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## New York State Common Core Math Grade 7, Module 4, Lesson 17

### Lesson 17 Student Outcomes

• Students write and use algebraic expressions and equations to solve percent word problems related to mixtures.

Lesson 17 Classwork

Opening Exercise
Imagine you have two equally sized containers. One is pure water, and the other is 50% water 50% and juice. If you combined them, what percent of juice would be the result?
If a 2-gallon container of pure juice is added to 3 gallons of water, what percent of the mixture is pure juice?
If a 2-gallon container of juice mixture that is 40% pure juice is added to 3 gallons of water, what percent of the mixture is pure juice?
If a 2-gallon juice cocktail that is 40% pure juice is added to 3 gallons of pure juice, what percent of the resulting mixture is pure juice?

Example 1
A 5-gallon container of trail mix is 20% nuts. Another trail mix is added to it, resulting in a 12-gallon container of trail mix that is 40% nuts.
a. Write an equation to describe the relationships in this situation.
b. Explain in words how each part of the equation relates to the situation.
c. What percent of the second trail mix is nuts?

Exercise 1
Represent each situation using an equation, and show all steps in the solution process.
a. A 6-pint 25% oil mixture is added to a 3-pint 40% oil mixture. What percent of the resulting mixture is oil?
b. An 11-ounce gold chain of 24% gold was made from a melted down 4-ounce charm of 50% gold and a golden locket. What percent of the locket was pure gold?
c. In a science lab, two containers are filled with mixtures. The first container is filled with a mixture that is 30% acid.
The second container is filled with a mixture that is 50% acid, and the second container is 50% larger than the first.
The first and second containers are then emptied into a third container. What percent of acid is in the third container?

Example 2
Soil that contains 30% clay is added to soil that contains 70% clay to create 10 gallons of soil containing 50% clay. How much of each of the soils was combined?

Exercise 2
The equation: (0.2)(x) + (0.8)(6 - x) = (0.4)(6) is used to model a mixture problem.
a. How many units are in the total mixture?
b. What percents relate to the two solutions that are combined to make the final mixture?
c. The two solutions combine to make six units of what percent solution?
d. When the amount of a resulting solution is given (for instance 4 gallons) but the amounts of the mixing solutions are unknown, how are the amounts of the mixing solutions represented?

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