Math Word Problems Demystified - A Self Teaching Guide

The amount of Mixture 1 equals the amount of Mixture 2. The amount to
be removed equals the amount to be added.

EXAMPLE:How much antifreeze which is 30% alcohol must be removed
from a 48-ounce container and replaced with water to make 48 ounces of a
solution which is 20% alcohol?

SOLUTION:

GOAL: You are being asked to find how much of the alcohol solution must
be removed and how much water must be added to dilute the solution.

STRATEGY: Letx¼the amount of the alcohol solution to be removed and
the amount of water to be added; then

Mixture 1
Amount to beþAmount of weaker mixture¼Mixture 2

removed to be added

30%(48)
30%(x)þ0%(x)*¼20%(48)

*Since the water has no alcohol, 0% is used.

IMPLEMENTATION: Solve the equation:

30 %ð 48 Þ
 30 %xþ 0 %ðxÞ¼ 20 %ð 48 Þ

0 : 30 ð 48 Þ
 0 : 30 %x¼ 0 : 20 ð 48 Þ

14 : 4 
 0 : 3 x¼ 9 : 6

14 : 4 
 14 : 4 
 0 : 30 x¼ 9 : 6 
 14 : 4

 0 : 30 x¼
 4 : 8

 0 : 301 x


 0 : 301

¼

4 : 8

0 : 30

x¼16 ounces

Hence to dilute the 30% solution, 16 ounces must be removed and
16 ounces of water must be added to make 48 ounces of a 20% solution.

LESSON 14 Solving Mixture Problems 151