Question

a 16 foot piece of wood was cut into two pieces. the longer of is 3 feet less than twice the shorter piece. what is the length of the longer piece of wood?

Answer 1

`\begin{gathered} shorter=(19)/(3)\text{ ft} \\ \text{longer }=(29)/(3)\text{ ft} \end{gathered}`

Step-by-step explanation

Step 1

Let

total length(purple line)= 16 feet

shorter piece= x

twice the shorter piece=2x

the longer piece= y

the longer is 3 feet less than twice the shorter piece.( in other words you have to add 3 to the longer pice to obtain twice the shorter piece)

`\begin{gathered} y+3=2x \\ y=2x-3\text{ Equation (1)} \end{gathered}`

Also

shorter piece+longer piece = full wood piece

replacing

`x+y=16\text{ Equation (2)}`

Step 2

fin x and y , using Equation (1) and (2)

i)repace equation (1) in equation (2)

`\begin{gathered} y=2x-3\text{ Equation (1)} \\ x+y=16\text{ Equation (2)} \\ repplace \\ x+2x-3=16 \\ 3x-3=16 \\ 3x=16+3 \\ x=(19)/(3) \end{gathered}`

ii)

replace the value of x in equation (1) to find y

`\begin{gathered} y=2x-3\text{ Equation (1)} \\ y=2\cdot(19)/(3)-3 \\ y=(38)/(3)-3 \\ y=(29)/(3) \end{gathered}`

I hope this helps you