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INEQUALITIES IN 2-VARIABLES
WORD PROBLEMS
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SETTING UP A SYSTEM FROM A WORD PROBLEM
Michelle and Ashley have a jewelry stand at the Bloomsburg Fair where they sell handmade bracelets and earrings. A bracelet sells for $8 and a pair of earrings for $10. The girls need to make at least $500 on the sale of their jewelry. The girls brought less than 100 total pieces of jewelry with them to sell. Set up a systems of inequalities modeling the this scenario where x = the number of bracelets and y = the number of earrings SETTING UP A SYSTEM FROM A WORD PROBLEM
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Total Cost & Total Quantity!
8x + 10y ≥ 500 x + y < 100 Total Cost & Total Quantity!
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QUESTIONS USING ONLY ONE EQUATION
If the girls only sell 10 pairs of earrings, at least how many bracelets would they need to sell to reach their goal of $500? Use the cost inequality only! 8x + 10y ≤ 500 8x + 10(10) ≤ 500 8x ≤ 500 8x ≤ 400 x ≤ (The girls must sell at least 50 bracelets) QUESTIONS USING ONLY ONE EQUATION
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QUESTIONS USING ONLY ONE EQUATION
What is the least number of pairs of earrings they need to sell if they only sold earrings to reach their goal of $500? Use the cost inequality only! 8x + 10y ≤ 500 8(0) + 10y ≤ 500 10y ≤ 500 y ≤ (The girls must sell at least 50 earrings) QUESTIONS USING ONLY ONE EQUATION
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SOLVING THE SYSTEMS BY GRAPHING
STEP 1: SOLVE EACH EQUATION FOR Y 8x + 10y ≥ 500 x + y < 100 y ≥ -4/5x + 50 y < -x + 100 SOLVING THE SYSTEMS BY GRAPHING
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SOLVING THE SYSTEM BY GRAPHING
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SOLVING THE SYSTEM BY GRAPHING
y < -x + 100 1 number of earrings 3 y ≥ -4/5x + 50 2 number of bracelets
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SETTING UP A WORD PROBLEM
The boys and girls soccer teams are doing a combination fundraiser for new uniforms. The boy’s team is selling candy bars for $2 each and the girl’s team is selling candles for $4 each. The must raise more than $800. The girl’s team is confident that they can sell at least 100 candles. Set up a systems of inequalities representing this situation where x represents the number of candy bars sold and y represents the number of candles sold. Graph both inequalities and shade the intersection. Give 2 possible solutions to this system. SETTING UP A WORD PROBLEM
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Set up the system and solve for “y”
2x + 4y > 800 y ≥ 100 y > -1/2x + 200 Set up the system and solve for “y”
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GRAPH THE SYSTEMS number of candles sold number of candy bars sold
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