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4-20.
ONE EQUATION OR TWO?
Elsie took all of her cans and bottles from home to the recycling plant. The number of cans was one more than
four times the number of bottles. She earned 12¢ for each bottle and 10e for each can, and ended up earning $2.18
in all. How many cans and bottles did she recycle?
Solomon decided to solve the problem by writing one equation. He said, "I con ler b represent the number of
bottles. Then 46+1 would be the member of cans. My equation would be 126 + 10(46 + 1) -- 218."
Marcus agreed with Solomon's answer, but said, "It is easier to solve this problem with no equations. I can let b
represent the number of bottles and c represent the number of cans. That wory ny two equations are
c=15+ 1 and 12b10c = 218.
a. Solomon's equation has three terms: 126. 10(46 + 1), and 218. What do each of these terms represent in the problem?
b. What do the parts of each of Marcus' equations represent?
c. Do Solomon's equation and Marcus' equations represent the same problem? Why or why not?
d. Solve this problem using Solomon's equation. Be sure to label your answer. You do not need to solve Marcus' equations.