Discover new perspectives and gain insights with IDNLearn.com's diverse answers. Discover reliable and timely information on any topic from our network of experienced professionals.

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.

Sagot :

3.75 ft and 1.25 ft

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

[tex]x+y=5\Rightarrow equation(1)[/tex]

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

[tex]x=3y\Rightarrow equation(2)[/tex]

Step 3

finally, solve the equations:

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

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

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

[tex]\begin{gathered} x=3y\Rightarrow equation(2) \\ x=3(1.25) \\ x=3.75 \end{gathered}[/tex]

therefore, the lengths of the pieces are

3.75 ft and 1.25 ft

I hope this helps you

View image RaulM535786
Thank you for using this platform to share and learn. Don't hesitate to keep asking and answering. We value every contribution you make. Thank you for visiting IDNLearn.com. We’re here to provide accurate and reliable answers, so visit us again soon.