Question

a 342-inch pipe is cut into two pieces one piece is five times the length of the other. Find the lengths of the two pieces​

Answer 1

285 and 57

Explanation:

First, find the length of the longer pipe, which is stated to be 5 times longer than the shorter piece. Substitute the longer piece as b. Same for the shorter piece, but as a.

`a + b = 342\\5b\:+\:? = 342\\a = 5b`

Why a is 5b is because a is the correspondent value to b since they are both substituted, in short words this means that a will be the equivalent of |5 × b - 342|

Next, we substitute the problem in a ruled equation. Think of it this way: There are 2 values in the equation. One has a value of 5 and the other has a value of one. Add those together, and you get 6, right? This will be important for our final answer.

`6b/ 6 = 342/ 6\\b = 57`

Lastly, substitute a.

`a + b = 342\\a + \bold{57} = 342\\a = \left(342 - 57\right)\\\\a = 285\\b = 57`

Hope this helps!