Lemonade Stand

John has a lemonade stand. He sells a small lemonade for 50 cents and a large lemonade for \$1. A small serving contains 1 cup of lemonade; a large contains 1.5 cups. At the end of the day, John has made \$9 and sold 15.5 cups of lemonade. How many small and large lemonades has he sold?
Source: NCTM Mathematics Teacher, September 2006

Solution
Let x represent the number of small lemonades and y the number of large lemonades sold. We have the following system of equations
x(.50)+y(1)=9\qquad\qquad\; (1)
x(1)+y(1.5)=15.5\qquad\quad\, (2)
Multiply Eqs. (1) and (2) by 2
x+2y=18\qquad\quad\:\: (3)
2x+3y=31\qquad\quad (4)
Multiply Eq. (3) by -2 and add to Eq. (4)
-2x-4y=-36
2x+3y=31
————————-
-y=-5
y=5
Substitute the value of y=5 into Eq. (3)
x+2(5)=18
x=8
John has sold 8 small and 5 large lemonades.

Answer: 8 small and 5 large

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About mvtrinh

Retired high school math teacher.
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