Math Word Problems Demystified - A Self Teaching Guide

alcohol. How much of each should be mixed to get 20 ounces of a solution

which is 8% alcohol?

SOLUTION:

GOAL: You are being asked to find the amounts of each solution that need

to be mixed to get 20 ounces of an 8% solution.

STRATEGY: Letx¼the amount of the 10% solution and 20
 x¼the

amount of the 5% solution; then set up a table as follows:

Amount  Percent ¼ Amount of pure

Mixture 1 x 10% 10%x

Mixture 2 20 
x 5% 5%(20
x)

Mixture 3 20 8% 8%(20)

The equation is

Mixture 1 þ Mixture 2 ¼Mixture 3

10 %x þ 5 %ð 20 
xÞ¼ 8 %ð 20 Þ

IMPLEMENTATION: Solve the equation:

10%xþ5%(20
x)¼8%(20)

Change the percents to decimals before solving the equation.

0 : 10 xþ 0 : 05 ð 20 
xÞ¼ 0 : 08 ð 20 Þ

0 : 10 xþ 1 
 0 : 05 x¼ 1 : 6

0 : 05 xþ 1 ¼ 1 : 6

0 : 05 xþ 1 
 1 ¼ 1 : 6 
 1

0 : 05 x¼ 0 : 6

148 LESSON 14 Solving Mixture Problems