John has a lemonade stand. He sells a small lemonade for cents and a large lemonade for . A small serving contains cup of lemonade; a large contains cups. At the end of the day, John has made and sold cups of lemonade. How many small and large lemonades has he sold?
Source: NCTM Mathematics Teacher, September 2006
Let represent the number of small lemonades and the number of large lemonades sold. We have the following system of equations
Multiply Eqs. and by
Multiply Eq. by and add to Eq.
Substitute the value of into Eq.
John has sold small and large lemonades.
Answer: small and large