A board 60 in. long is cut into two parts so that the longer piece is 5 times the shorter. What are the lengths of the two pieces?

Question

how do i solve, A board 60 in. long is cut into two parts so that the longer piece is 5 times the shorter. What are the lengths of the two pieces?

Answer 1

Step 1) Let's think it through.

 

Alright so we have two unknown pieces of wood that will, if added together, equal 60 inches. Next, the two pieces are different sizes. One is 5 times shorter than the other. 

 

Step 2) Let's get some variables. We'll call the short piece x and the long one y

 

Step 3) Let's get some equations. x + y = 60 which just means piece one plus piece two equals 60. And if x is the short one, then x = 5y. Meaning y is 5 times longer than x. Or x is shorter than y. Now we have a system of equations: 

 

x + y = 60

x = 5y

 

Step 4) Solve. There are different ways to solve systems of equations (e.g. substitution/elimination). In this case, we can substitute. 

 

(5y) + y = 60 (substituting the x = 5y). 

 

therefore 6y = 60, and so y must be 10. We can plug this into x = 5y to get the final answer. 

 

Best, 

Robert

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