3.2
Solving APPLICATIONS
(WORD PROBLEMS)
using
Systems of Equations
There are 4 ways to solve
Systems of Equations
1. Graphing
2. Substitution Method
3. Addition­Subtraction Method
(aka elimination)
4. Multiplication­Addition Method
(aka elimination)
Set up a system of equations for the following and solve:
1)
Shopping at Savers Mart, Lisa buys her children 5 shirts and 2 pairs of pants for $75. She returns the next day and buys 3 shirts and 4 pairs of pants for $100. If s represents shirts and p represents pants, which of the following systems can be solved to correctly determine the price of a shirt and a pair of pants? 2) Shopping at Savers Mart, Lisa buys her children four shirts and three pairs of pants for $85.50. She returns the next day and buys three shirts and five pairs of pants for $115.00. What is the price of each shirt and each pair of pants.
step 1: define your variables
step 2: Write 2 equations­­ one for first sentence and one for second sentence. step 3: Solve for your variables
step 4: Write the answer using words
Set up a system of equations for the following and solve:
3) Anthony and Ann bought some pens and pencils. Anthony bought 4 pens and 5 pencils, which cost him $6.71. Ann bought 5 pens and 3 pencils, which cost her $7.12. Let x equal the price of a pen. Let y equal the price of a pencil. Find the price of a pen and find the price of a pencil.
1
4) Suppose you bought supplies for a party. 3 rolls of streamers and 15 party hats cost $30. Later, you bought 2 rolls of streamers and 4 party hats for $11. How much did each roll of streamers cost? How much did each party hat cost?
5) The Math club and the Science Club had a fundraiser to buy supplies for a local food pantry. The math club spent $135 buying 6 cases of juice and 1 case of bottled water. The science club spent $110 buying 4 cases of juice and 2 cases of bottled water. How much did a case of juice cost? How much did a case of bottled water cost?
j= juice 4 (6j+1w=135)
w=water ­6 (4j+2w=110) 24j+ 4w = 540 4j+2w=110
­24j­12w=­660
­8w=­120
­8 ­8
w=15
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6) Suppose you bought supplies for a party. 3 rolls of streamers and 14 party hats cost $40. Later, you bought 2 rolls of streamers and 4 party hats for $16. How much did each roll of streamers cost? How much did each party hat cost?
7)
You sold 21 boxes of candy for your club's fundraiser. The large size box costs $10.00 each and the small size box costs $4.50 each. If you sold $144.00 worth of candy, how many large boxes did you sell?
number of
large boxes = 9
8
8) You sold 17 candles for your club's fundraiser. The large candle costs $10.50 each and the small candle costs $5.75 each. If you sold $150.00 worth of candles, how many large candles did you sell?
number of large
candles =
8