Question

Carlos is helping his son with a lemonade stand. They have 200 cups, size large and small. The large cups sell for $2, and the small for $1. At the end of the weekend, they have used all their cups and have $340. How many of each size did they sell?

Answer 1

Anthony T. answered • 03/17/21

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First, let's ask ourselves what do we want to know? We want to know how many cups of small and large lemonades were sold. Let's let S = # of small cups, and L the # of large cups.

It says she sold a total of 155 cups; that means S + L = 155. So this is one equation.

Next it says she made a total of $265. The small cups sold for $1.25 each, so she made $1.25S amount of money on these. It also says she sold large cups for $2.50 each, so she made $2.50L on these.

So, if we add up the money she made from each size, we can say 1.25S + 2.50L = 265.

Now we have two equations with 2 unknowns, and we can solve by either elimination or substitution. Let's solve it by substitution.

As S + L =155, L = 155 - S. Put this expression for L into the second equation.

1.25S + 2.50(155-S) = 265. Now solve this for S.

You should get S = 98 small cups. So, from the equation S + L = 155, solve for L which gives

L = 57 large cups. You can prove this by substituting these numbers in the second equation.

The same principles apply to other problems of this type.