A child in a neighborhood had a lemonade stand where large cups sold for $0.75, medium cups sold for $0.60 and small cups for $0.45.on Saturday a total of 78 cups were sold for $46.95. The number of mediumcups sold was 4 less than the sum of the large and small cups. What is a system of equations that can be used to find how many of each did the child sell?

The problem statement asks for the number of each size cup sold. You are told there are three sizes, so it is convenient to use one variable to represent the number of cups of a given size that were sold—three variables total.The problem statements tell you the relationships between the numbers:

the total number of cups sold
the total value of cups sold
the relationship between numbers of one size versus other sizes

It is appropriate to write an equation for each of these relationships, for a total of three equations. (Here, the last of these equations is put into standard form to make it easier to translate this to a matrix equation for solving by calculator.)

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The solution is: 20 small, 37 medium, and 21 large.