10-810-8Mixture ProblemsMixture Problems

Standard 15.0: Apply algebraic Standard 15.0: Apply algebraic techniques to percent mixture techniques to percent mixture

problems.problems.

VocabularyVocabulary Problem-Solving GuidelinesProblem-Solving Guidelines

UNDERSTAND the problemUNDERSTAND the problem Develop and carry out a PLANDevelop and carry out a PLAN Find the ANSWER and CHECKFind the ANSWER and CHECK

#1 Solving Mixture Problems

poundper $1.60 Solution Second

lb.per $0.90 Solution First

Let x = The number of lbs of the first solution.

poundper $1.30 Solution Final

Let 175 – x = The number of lbs of the second solution.

A grocer wishes to mix some peanuts worth $0.90 per pound with some M&M’s worth $1.60 per pound to make 175 pounds of a mixture that is worth $1.30 per pound. How much of each should she use?

#1 Solving Mixture Problems

First Solution

Second Solution

Number of pounds

Price per pound

Amount of mixture

Final Solution

x

x17590.060.1

x90.0)175(6.1 x

5.2276.12809.0 xx5.527.0 x

lbs. 75x

175 30.1 )175(3.1

lbs. 100

acid 30% Solution Second

acid 60% Solution First

acid 50% Solution Final

#2 Solving Mixture Problems

Let x = amount of the first solution.

Let 750 – x = The amount of the second solution.

A chemist has one solution that is 60% acid and another that is 30% acid. How much of each solution is needed to make a 750 mL solution that is 50% acid?

#2 Solving Mixture Problems

First Solution

Second Solution

Amount of solution

Percent acid

Amount of acid

Final Solution

x

x750%60%30

x6.0)750(3.0 x

3753.02256.0 xx1503.0 xmL 500x

750 %50 )750(5.0

mL 502