The debate club needs $240.00 to attend a debate tournament. The club decides to sell cups of iced tea and lemonade at baseball games.

Question

Iced tea will be sold for $.50 per cup and lemonade will be sold for $.80 per cup. Graph the equation. Use your graph to find three different combinations of cups of iced tea sold and cups of lemonade sold that will raise $240.00.

The equation I got to graph was 0.5x+0.8y=240

Answer 1

I hate graphs, but it's simple to come up with 3 combinations algebraically. The least common multiple (LCM) of the prices is $4. I learned least common multiple and greatest common factor (GCF, also known as GCD for greatest common divisor) in elementary school and didn't use those terms after that, but LCMs and GCFs can be useful in later math.

1. 8 iced tea for $4, 295 lemonade for $236
2. 16 iced tea for $8, 290 lemonade for $232
3. 24 iced tea for $12, 285 lemonade for $228

The pattern can work in $4 increments from no iced tea and 300 lemonade to 480 iced tea and no lemonade. If I had to explain it, I would have the student write multiples of $.50 and multiples of $.80 to find the LCM. I would then have the student do $240/$4.