The length of a stick is 37 inches long. Peter breaks the stick so that one piece is 5 inches less than twice the length of the other piece. How long is each piece?

Answer 1

The way I would recommend you approach this problem is to set up a system of equations.

Let x=length of stick 1 and

y=length of stick 2

When the two sticks were together, their combined length was 37 inches meaning

x+y=37

Since we have two unknowns and only one equation, we need another. We also have the information that "one piece is twice the length of the other piece." To write this algebraically, we have

y=2x-5

Now that we have two equations and two unknowns, we can solve for x and y. One method would be substitution. Since we know y=2x-5, we can plug that in to the other equation giving us

x+(2x-5)=37

Now solve for x

3x=42

x=14

Now that we have x, we can quickly solve for y

y=2*14-5

y=23

Therefore, the lengths of the sticks are 14 and 23 inches.

Answer 2

Hi, Ashley!

This problem does sound very tricky when you first read it. But I would encourage you to draw a picture to try to figure it out.

First draw two lines to represent the two sticks that Peter has created. Notice how one of these sticks is simply described as "the other piece." That's all we know about the piece. This is a good sign that we should represent "the other piece" with a variable. Let's use x. So now one of your sticks is simply marked as a length of x.

Now move on to your remaining stick. It is described in terms of "the other piece," or x. This means that we can translate the verbal expression for this stick by replacing "the other piece" with x. The expression "5 inches less than twice the length of the other piece" can be translated into the math expression 2x - 5. Note, whenever the word "less than" is used you switch the order of the information. Even though 5 occurs before 2x in the verbal expression, less than makes us switch this order. Mark your remaining stick as 2x -5.

We know that both sticks combined equal 37 inches. When we combine things we are adding them together. So we can set up the following equation: x + 2x -5 = 37. You can solve this using basic algebra:

3x -5 = 37

3x = 42

x = 14

This tells us that "the other piece" marked with an x is 14 inches long. If we plug the value of x into 2x - 5... 2(14) - 5...we find that the remaining stick is 23 inches.

I hope this helps! Let me know if you have anymore questions.

Katie