College Algebra 9th txtbk

SECTION 1–1 Linear Equations and Applications 53
SOLUTION
Let x amount of 80% solution used.
BEFORE MIXING
AFTER MIXING
80% solution
20% solution
30% solution
x liters
5 liters
(x 5) liters
Amount of Amount of
Amount of
° alcohol in ¢ ° alcohol in ¢ ° alcohol in ¢
first solution second solution mixture
0.8x
Add 1 liter of the 80% solution.
0.2(5)
0.3(x 5)
0.8x 1 0.3x 1.5
0.5x 0.5
x 1
CHECK Liters of Liters of
solution alcohol Percent alcohol
First solution 1 0.8(1) 0.8 80 or 0.81
Second solution 5 0.2(5) 1 20 or 15
Mixture 6 1.8 1.86 0.3, or 30%
MATCHED PROBLEM 8
A chemical storeroom has a 90% acid solution and a 40% acid solution. How many centiliters
of the 90% solution should be added to 50 centiliters of the 40% solution to yield
a 50% solution?
ANSWERS TO MATCHED PROBLEMS
1. x 5 2. F 9 5C 32 3. 3, 5, 7 4. 20 centimeters
5. 50 minutes 6. 50 miles per hour 7. 3.6 hours 8. 12.5 centiliters
1-1 Exercises
1. What does it mean to solve an equation?
2. Describe the difference between an equation and an
expression.
3. How can you tell if an equation is linear?
4. In one or two sentences, describe what parts 1– 4 in Theorem 1
say about working with equations.
5. How can you check your solution to an equation?
6. How do you check your solution to a word problem?