Question

A carpenter cuts a 5-ft board in two pieces. One piece must be three times as longas the other. Find the length of each piece.

Answer 1

3.75 ft and 1.25 ft

Step-by-step explanation

Step 1

Diagram

Step 2

set the equations

let x represents the longest piece

lety represents the smaller piece

so

a)A carpenter cuts a 5-ft board in two pieces, hence

`x+y=5\Rightarrow equation(1)`

b)One piece must be three times as long as the other,then

`x=3y\Rightarrow equation(2)`

Step 3

finally, solve the equations:

a) replace the x value from equation (2) into equation(1)

`\begin{gathered} x+y=5\Rightarrow equation(1) \\ (3y)+y=5 \\ add\text{ like terms} \\ 4y=5 \\ divide\text{ both sides by 4} \\ (4y)/(4)=(5)/(4) \\ y=1.25 \end{gathered}`

b) now, replace the y value into equation (2) to find x

`\begin{gathered} x=3y\Rightarrow equation(2) \\ x=3(1.25) \\ x=3.75 \end{gathered}`

therefore, the lengths of the pieces are

3.75 ft and 1.25 ft

I hope this helps you