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Unit 5
Day 8
Applications of Linear Systems
Don’t Let Word Problems Get You Down…
Warm Up! Partner Think Tank…
How many variables will I need to identify and eventually solve for?
a. You decide to order some baseball cards from
an online catalogue. Each pack of cards you
order costs $3.50, and the shipping fee is a
flat $5.00 no matter how many cards you
order. If your order came to a total of $50.50,
how many packs of cards did you order?
b. Suppose you have just enough money, in
coins, to pay for a loaf of bread priced at
$1.95. You have 12 coins, all quarters and
dimes. How many quarters and how many
dimes were there?
What method would you use to solve a and b?
Let’s Practice!
The Problem:
On Monday, Joe bought 10 bagels and 5 doughnuts for
his Algebra I class at the cost of $16.50. It turns out
that the doughnuts were more popular than the
bagels. On Tuesday he bought 5 bagels and 10
doughnuts for a total of $14.25. What is the price for a
bagel and what is the price for a donut?
But where do I start? A few helpful hints…
 Read each word problem at least two to three
 Underline what you know and assign variables to
what you need to find.
 Write equation(s) for the situation:
o One equation – you only have one variable to
find. Solve using basic algebra.
o Two equations (a system) – you have two
variables to find; thus, you must write two
equations. Solve by graphing (intersection
point), elimination or substitution.
 Determine if your answer is reasonable. Plug your
solution back in – does it work??
Let’s solve!
Step 1: Identify the variable(s):
Step 2: Write your equation(s):
Step 3: Solve!
Step 4: Check!
A few more! Define your variables, set up your system and solve…
Example 1: Matt and June are selling boxes of fruit for a Habitat for Humanity fundraiser. Customers can buy small
boxes of fruit and large boxes of fruit. Matt sold 3 small boxes of fruit and 14 large boxes of fruit for a total of $203.
June sold 11 small boxes of fruit and 11 large boxes of fruit for a total of $220. Find the cost each of one small box
of fruit and one large box of fruit.
Example 2: The Bulls scored a total of 80 points in a basketball game against the Pacers. The Bulls made a total of
37 two point and three point baskets. How many two point shots did the Bulls make? How many 3 point shots did
the Bulls make?
Example 3: During a football game the parents of the Devils football players sell nachos and popcorn to raise
money for new uniforms. They charge $2.50 for nachos, and $2 for a bag of popcorn. The parents collect $336 in
sales during the game. They sell a total of 144 items. Set up a system of equations and solve to determine how
many nachos and bags of popcorn were sold.
Example 4: Find the value of two numbers if their sum is 12 and their difference is 4