two pieces of rope such once piece was 5 feet less than 3 times the other piece. Together they measured 51 feet. What is the length of each piece

Question

whenMichael was cleaning out his garage, he found two pieces of rope such once piece was 5 feet less than 3 times the other piece. Together they measured 51 feet. What is the length of each piece or rope

Answer 1

Hello, Sharon!

We need to set up an algebraic equation.

We know that the length, in feet, of piece(1)+piece(2)=51 feet. Let's call piece(1) P. The other piece, we are told, is 5 less than 3 times that other piece (which we called P); thus, we can express piece(2) as 3P-5.

This gives us the equation: P+3P-5=51.

Now, we shuffle stuff around:

P+3P-5=51
P+3P=56
4P=56
P=14

One piece is 14 feet, the other is (51-14) 37.

Hope this helps!

Answer 2

The first thing to do here is write out the problem with numbers and variables, so it's easier to see and understand. Let's use "r" for rope!

 

One rope is easy; it's simply represented by r. So let's focus on the second one. It's 5 feet less than 3 times more so that would translate to 3r-5.

 

Now you know that both of the ropes together equal 51 feet, so let's write that all together.

 

r + 3r - 5 = 51

 

Now combine the variables.

 

4r -5 = 51

 

Add 5 to both sides of the equation.

 

4r = 56

 

Divide both sides by 4.

 

r = 14

 

Now this is important, but we're not done yet! We need to substitute r for the length of each rope.

 

Rope 1: r = 14'

 

Rope 2: 3r - 5 = 3(14) - 5 = 42 - 5 = 37'