M1H Lesson 6.1.4 Solving Word Problems by Writing Equations

Mathematical sentences, like those in the left column of the last problem, are easier to understand when everyone knows what the variables represent. A statement that describes what the variable represents is called a “let” statement. For example, we could say, “Let d=total distance driven in miles.” Note that a let statement always indicates the units of measurement.

Write a let statement for each of the mathematical sentences in problem 1:

Elsie took all of her cans and bottles from home to the recycling center. The number of cans was one more than four times the number of bottles. She earned 12¢ for each bottle and 10¢ for each can, and ended up earning $2.18 in all. How many cans and bottles did she recycle?

Elsie took all of her cans and bottles from home to the recycling center. The number of cans was one more than four times the number of bottles. She earned 12¢ for each bottle and 10¢ for each can, and ended up earning $2.18 in all. How many cans and bottles did she recycle?

After reading about earning money by recycling, Solomon and Marcus are excited to do some recycling themselves.

Solomon has some electronics his parents said he could recycle. Marcus has permission to recycle some small household appliances. They looked online and discovered that the local recycling center offers $0.60 per pound for the appliances and $1.50 per pound for the electronics. But there is a $27 hazardous waste fee that has to be paid to recycle electronics, no matter how much you recycle.