Willa R. answered • 02/16/17
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Experienced, Skilled Educator & Renaissance Woman, PhD in Physics
To solve this one, the key is understanding that there are two variables, or unknowns, involved: the lengths of the two pieces. Let's call one length in inches x and the other y.
For two unknowns, you must have two equations to work with in order to know the value of either one. Therefore, we need to find two constraints on lengths x and y and translate them into mathematics.
First constraint: If you cut a rope in two pieces, the first piece's length and the second piece's length must add up to the original length.
x+y=52
The next is the constraint that the problem states outright. One piece must be three times as long as the other. It does not matter if you call the longer piece x or y. I will choose y. This gives the second equation.
y=3x
We can therefore substitute the expression for y into the first equation.
x+3x=52
or
4x=52
We can divide both sides by 4 to get x. 52 divided by 4 is 13. So x=13
Knowing that y=3x, we can then say that y=3*13=39.
I encourage you to try working the problem with x as the longer piece as well.
For two unknowns, you must have two equations to work with in order to know the value of either one. Therefore, we need to find two constraints on lengths x and y and translate them into mathematics.
First constraint: If you cut a rope in two pieces, the first piece's length and the second piece's length must add up to the original length.
x+y=52
The next is the constraint that the problem states outright. One piece must be three times as long as the other. It does not matter if you call the longer piece x or y. I will choose y. This gives the second equation.
y=3x
We can therefore substitute the expression for y into the first equation.
x+3x=52
or
4x=52
We can divide both sides by 4 to get x. 52 divided by 4 is 13. So x=13
Knowing that y=3x, we can then say that y=3*13=39.
I encourage you to try working the problem with x as the longer piece as well.
