Math: word problems: “let” statements

Tutoring math, word problems come up. The tutor gives an example of “let” statements.

Problem: A 207cm rope is cut in two pieces, one 15cm longer than the other. How long is each piece?

Solution: “let” statements are used to express a word problem so that it can be written as an equation. Normally we “let” the variable be one of the items we don’t know but want to find. In this case, we want to find both lengths of rope the 207cm one was cut into.

let x = the shorter piece of rope

let x + 15 = the longer piece //this defines it as 15cm longer

Note that both the unknown lengths of rope are expressed using the same variable. The shorter is x alone, while the other, being 15cm longer, is x + 15.

Next, we write the equation, based on the idea that we know the two lengths add to 207cm:

x + x + 15 = 207

2x + 15 = 207

Subtracting 15 from both sides gives

2x = 192

Dividing both sides by 2 we get

x = 96

So, the shorter piece of rope is 96cm. The other let statement, x + 15, tells us the longer piece is 96 + 15 = 111cm.

Source:

Traverse, Kenneth J. et al. Using Advanced Algebra. Toronto: Doubleday Canada Limited, 1977.