Chapter 5: Linear Systems Name
Section 2: Using Algebra Date
Topics in Algebra 1 © 2001, 2002 Texas Instruments Student Worksheet 5-19
2. Cathy decides to spend some of her earnings from her new job, so she and her friend
Brenda go to the mall. Their favorite store has blouses and jeans on sale. A variety of
blouses is on one rack and are all the same price. A variety of jeans is on another rack and
are all the same price. The price tags are not on the clothes but Cathy and Brenda know that
the store’s prices are usually within their budgets.
Cathy picks out 3 blouses and 2 pairs of jeans from the sale racks. At the checkout, she sees
that her total bill is $57.00. Brenda picks out 4 blouses and 3 pairs of jeans from the sale
racks. Her total bill is $81.00. They are shopping in the state of Delaware where there is no
sales tax.
To find the cost of one blouse or one pair of jeans, Cathy and Brenda could just look at the
sales receipt. Instead, they try to figure out the prices themselves.
•
Write the system of equations that Cathy and Brenda need to solve. Clearly define the
variables and their meaning.
• Solve the system of equations using elimination. Show your work and explain the steps
you used to solve the system of equations. Show the check of your solution.
Hint: You can multiply both equations by a factor to avoid working with fractions!
• Write a sentence explaining the price Cathy and Brenda paid for each top and each pair
of jeans.
Remember: You always have a choice of picking the method that you think will be easiest to perform when solving systems
of equations. In the problems above, you are asked to use a specific method.
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