INEQUALITIES IN 2-VARIABLES WORD PROBLEMS

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

Total Cost & Total Quantity! 8x + 10y ≥ 500 x + y < 100 Total Cost & Total Quantity!

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 + 100 ≤ 500 8x ≤ 400 x ≤ 50 (The girls must sell at least 50 bracelets) QUESTIONS USING ONLY ONE EQUATION

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 ≤ 50 (The girls must sell at least 50 earrings) QUESTIONS USING ONLY ONE EQUATION

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

SOLVING THE SYSTEM BY GRAPHING

SOLVING THE SYSTEM BY GRAPHING y < -x + 100 1 number of earrings 3 y ≥ -4/5x + 50 2 number of bracelets

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

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”

GRAPH THE SYSTEMS number of candles sold number of candy bars sold