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# Maths help pls!

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Larry's Lemons is a street vendor business that sells lemonade and lemon bars. A cup of lemonade sells for \$2 and a lemon bar sells for \$1.50. When all related business expenses are included, a cup of lemonade costs \$0.25 to prepare and a lemon bar costs \$0.20 to prepare.

Last Monday, one of the vendors selling Larry's Lemons sold at least \$500 worth of lemonade and lemon bars and its expenses were no more than \$100. At least 150 cups of lemonade were sold.

Let x be the number of cups of lemonade sold last Monday and y be the number of lemon bars sold last Monday.

Which ordered pairs representing a combination of cups of lemonade and lemon bars could have been sold last Monday and make sense in the context of the situation?

(160,110)(160,110)

(232.5,200)(232.5,200)

(155,305.5)(155,305.5)

(150,200)(150,200)

(180,100)

Oct 3, 2018

#1
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You have the following inequalities:

\(2x+1.5y\ge500\\0.25x+0.2y\le100\\x\ge150\)

Plug in the various pairs of x and y (eg x = 160, y = 110;  x = 232.5, y = 200; ...etc.) and see which pairs satisfy these inequalities.

(Strangely, it looks as though it's possible to sell a half cup of lemonade and half a lemon bar!  Unless, of course, they are clues to impossible outcomes!)

Oct 3, 2018
edited by Alan  Oct 3, 2018
#2
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Using Alan's inequalities....look at the graph, here : https://www.desmos.com/calculator/f0gvhes7s3

Assuming the 1/2 cups of lemonade and 1/2 lemon bars can't be possibilities...the answers that make sense lie in the feasible region of the overlap of the graphs...these are    (150, 200)  and  ( 180, 100 )

Oct 3, 2018