Intermediate Algebra (11th edition)

Step 4 Solvethe system. To eliminate h, multiply equation (2),

by and add.

(1)

Multiply each side of (2) by.

Add.

Divide by.

To find the value of h, let in equation (2).

(2)

Let

Multiply.

Subtract 98.94.

Step 5 State the answer.The average price for one basketball ticket was $49.47.

For one hockey ticket, the average price was $49.66.

Step 6 Checkthat these values satisfy the conditions stated in the problem.

NOW TRY

OBJECTIVE 3 Solve mixture problems by using two variables.We solved

mixture problems in Section 2.3using one variable. Many mixture problems can also

be solved using more than one variable and a system of equations.

Solving a Mixture Problem

How many ounces each of 5% hydrochloric acid and 20% hydrochloric acid must be

combined to get 10 oz of solution that is 12.5% hydrochloric acid?

Step 1 Readthe problem. Two solutions of different strengths are being mixed

together to get a specific amount of a solution with an “in-between” strength.

Step 2 Assign variables.

Let the number of ounces of 5% solution

and the number of ounces of 20% solution.

Use a table to summarize the information from the problem.

y=

x=

EXAMPLE 3

h=49.66

h+98.94=148.60

h+ 21 49.47 2 =148.60 b=49.47.

h+ 2 b=148.60

b=49.47

b= 49.47 - 3

- 3 b=-148.41

- 2 h- 4 b=-297.20 - 2

2 h+ b= 148.79

- 2

h+ 2 b=148.60,

236 CHAPTER 4 Systems of Linear Equations

NOW TRY
EXERCISE 2
For the 2009–2010 season at
Six Flags St. Louis, two gen-
eral admission tickets and
three tickets for children un-
der 48 in. tall cost $172.98.
One general admission ticket
and four tickets for children
under 48 in. tall cost $163.99.
Determine the ticket prices
for general admission and for
children under 48 in. tall.
(Source:www.sixflags.com)

Gives Gives

equation (1) equation (2)

Multiply the amount of each

solution (given in the first column)

by its concentration of acid (given

in the second column) to find the

amount of acid in that solution

(given in the third column).

Ounces of Percent Ounces of

Solution (as a decimal) Pure Acid

x 0.05x

y 0.20y

10 12.5%=0.125 1 0.125 210

20 %=0.20

5 %=0.05

Ounces of

solution

Ounces of

pure acid

x

0.05x

+

y

0.20y

=

10

0.125 (10)

Gives equation (1)

Gives equation (2)

FIGURE 9

FIGURE 9illustrates what is happening in the problem.

NOW TRY ANSWER

2. general admission: $39.99;
   children under 48 in. tall: $31.00