Sasha and Francisco were selling lemonade for 25 cents per half cup and 50 cent per full cup. At the end of the day they had collected 17 dollars and had used 37 cups. How many full cup and how many half cups did they sell?

Solution

Let x be the number of full cup sold

Let y be the number of half cup sold

Whether the cup was full or not, they used 37 cups.

Therefore,

x + y = 37

How much money did they make selling half cup lemonade?

How much money did they make selling full cup lemonade?

Money made selling full cup + money made selling half cup = 17

x × 0.50 + y × 0.25 = 17

You end up with a system of linear equation to solve

x + y = 37

x × 0.50 + y × 0.25 = 17

x + y = 37 equation 1

0.50x + 0.25y = 17 equation 2

Solve for y in equation 1

x + y = 37

x - x + y = 37 - x

y = 37 - x

Replace y in equation 2

0.50x + 0.25 (37 - x) = 17

0.50x + 0.25 × 37 - 0.25x = 17

0.50x + 9.25 - 0.25x = 17

0.25x + 9.25 = 17

0.25x + 9.25 - 9.25 = 17 - 9.25

0.25x = 17 - 9.25

0.25x = 7.75

Divide both sides by 0.25

0.25x/0.25 = 7.75/0.25

x = 31

y = 37 - x = 37 - 31 = 6

Sasha and Francisco sold 31 full cup and 6 half cup of lemonade.

It seems like people love their lemonade!

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