Systems of Inequalities Jeopardy Challenge
Engage in a fun Jeopardy game created by Myia, Erin, and Maddy focusing on solving systems of inequalities. Test your math skills with interactive questions ranging from determining variable values to graphing systems. Challenge yourself with different point levels and categories for an exciting learning experience.
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Presentation Transcript
SYSTEMS OF INEQUALITIES JEOPARDY By Myia, Erin, and Maddy
Category 1 Category 2 Category 3 200 200 200 200 200 300 300 300 300 300 300 400 400 400 400 400 400
CATEGORY 1 200 POINTS What is the value of Y in the equation when X =0 Y<X+6 Answer
Y<6 Home Home
Category 1 300 Points What is the Y value of Y>6X-5 when X=2 Answer
Category 1 300 points Y>7 Home Home
CATEGORY 1 400 POINTS What is the value of Y in the Equation Y>X15+-5 when X=10 Answer
Category 1 400 Points Y>145 Home Home
CATEGORY 2 200 POINTS Solve the system by graphing it 2x 3y < 12 x + 5y < 20 x > 0 Answer
Category 2 200 Points Home Home
CATEGORY 2 300 POINTS Solve the system by graphing it 2x y > 3 4x + y < 5 Answer
Category 2 300 points Home Home
CATEGORY 2 400 POINTS Solve the system by graphing it x y < 2 x y > 2 Answer
Category 2 400 Points No Solution Home Home
CATEGORY 3 200 POINTS A calculator company produces a scientific calculator and a graphing calculator. Long-term projections indicate an expected demand of at least 100 scientific and 80 graphing calculators each day. Because of limitations on production capacity, no more than 200 scientific and 170 graphing calculators can be made daily. To satisfy a shipping contract, a total of at least 200 calculators much be shipped each day. If each scientific calculator sold results in a $2 loss, but each graphing calculator produces a $5 profit, how many of each type should be made daily to maximize net profits? Answer Answer
Category 3 200 points x: number of scientific calculators produced y: number of graphing calculators produced Y=170 X=200 X=100 Y=80 Y=-X+200 Home Home
CATEGORY 3 300 POINTS You have $12,000 to invest, and three different funds from which to choose. The municipal bond fund has a 7% return, the local bank's CDs have an 8% return, and the high-risk account has an expected (hoped-for) 12% return. To minimize risk, you decide not to invest any more than $2,000 in the high-risk account. For tax reasons, you need to invest at least three times as much in the municipal bonds as in the bank CDs. Assuming the year-end yields are as expected, what are the optimal investment amounts? Answer Answer
Category 3 300 Points x: amount (in thousands) invested in bonds y: amount (in thousands) invested in CDs Maximize Y = 1.44 0.05x 0.04y, subject to: x > 0 y > 0 y > x + 10 y < x + 12 y < (1/3)x Home Home
Explanation Since the question is asking to find the amount of money for each account, the variables will need to stand for those amounts. Since its easier to deal with smaller numbers, count by thousands x: amount (in thousands) invested in bonds y: amount (in thousands) invested in CDs only have two variables, but have three accounts. To handle this, they need the How much is left" construction: 12 x y: amount (in thousands) invested in the high-risk account can't invest negative amounts of money, so the first two constraints are the usual ones: x > 0and y > 0. The amount in the high-risk account can't be negative either, so 12 x y > 0, which simplifies as: y < x + 12 The upper limit on the high-risk account gives the inequality (12 x y) < 2. This simplifies as: y > x + 10 And the tax requirements give y < (1/3)x. The optimization equation will be the total investment yield, Y = 0.07x + 0.08y + 0.12(12 x y) = 1.44 0.05x 0.04y.
CATEGORY 3 400 POINTS The "We Sell CDs" website plans to purchase ads in a local newspaper advertising their site. Their operating budget will allow them to spend at most $2200 on this advertising adventure. They plan to run at most 20 ads. An ad will cost $50 to appear in the weekday paper and $200 to appear in a weekend edition. Prepare a graph that will represent all of the possible combinations of ads under these conditions Answer Answer
Category 3 400 Points x + y < 20 (there will be at most 20 ads) 200x + 50y < 2200 (the cost of the ads at most $2200) Home Home
