Beginning Algebra, 11th Edition

SECTION 4.4 Applications of Linear Systems^273

Step 5 State the answer.Footwear sales were $17,190 million and clothing sales

were $10,563 million.

Step 6 Checkthe answer in the original problem. Since

and

the answer satisfies the information in the problem. NOW TRY

CAUTION If an applied problem asks for twovalues, as in Example 1,be sure

to give both of them in your answer.

OBJECTIVE 2 Solve problems about quantities and their costs.

Solving a Problem about Quantities and Costs

For a production of the musical Wickedat the Ford Center in Chicago, main floor

tickets cost $148, while the best balcony tickets cost $65. Suppose that the members

of a club spent a total of $2614 for 30 tickets to Wicked. How many tickets of each

kind did they buy? (Source:www.ticketmaster.com)

Step 1 Readthe problem several times.

Step 2 Assign variables.

Let the number of main floor tickets,

the number of balcony tickets.

Summarize the information given in the problem in a table.

and y=

x=

EXAMPLE 2

17,190-10,563 = 6627 17,190+ 10,563=27,753,

NOW TRY
EXERCISE 1
Marina Polyakova pays a total
of $1150 per month for rent
and electricity. It costs $650
more for rent per month than
for electricity. What are the
costs for each?

NOW TRY ANSWER
1.rent: $900; electricity: $250

Number Price per Ticket Total

of Tickets (in dollars) Value

Main Floor x 148 148 x

Balcony y 65 65 y

Total 30 2614

The entries in the first two rows of

the Total Value column were found

by multiplying the number of tickets

sold by the price per ticket.

Step 3 Write two equations.

Total number of tickets was 30. (1)

Total value of tickets was $2614. (2)

Step 4 Solvethe system from Step 3 using the elimination method.

Multiply equation (1) by.

(2)

Add.

Divide by 83.

Substitute 8 for xin equation (1).

(1)

Let

y= 22 Subtract 8.

8 +y= 30 x=8.

x+y= 30

x= 8

83 x = 664

148 x+ 65 y= 2614

- 65 x- 65 y=- 1950 - 65

148 x+ 65 y= 2614

x+ y= 30