Question 159181: Write and solve a system of inequalities for a given model / word problem.
1. Manuel’s lunch cart sells burritos and chili. To stay in business, Manuel must sell at least 10 orders of chili and 30 burritos per day. Because of limited space, not more than 40 orders of chili or 70 burritos can be made. The total number of orders cannot exceed 90. If Manuel decides to sell 30 burritos, what is the greatest and fewest number of chili orders he can sell?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Manuel’s lunch cart sells burritos and chili. To stay in business,
Manuel must sell at least 10 orders of chili and 30 burritos per day.
c >= 10
b >= 30
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Because of limited space, not more than 40 orders of chili or 70 burritos can be made.
10 <= c <= 40 (This defines the domain of the function)
30 <= b <= 70 (This defines the range of the function)
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The total number of orders cannot exceed 90.
b + c <= 90
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If Manuel decides to sell 30 burritos, what is the greatest and fewest number of chili orders he can sell?
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b = 30
Since b+c <=90, 30 + c <= 90; c <= 60 (greatest number of chili orders)
Since 10 <= c <=40, c >= 10 (least number of chili orders)
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Cheers,
Stan H.
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