Question

A carpenter cut four lengths of wood. The lengths were 36 3/4th in., 36 3/8th in., 37 1/2 in., and z in. If the mean of the lengths is 36 5/8th in., what was the length of the fourth piece of wood the carpenter cut?

Answer 1

`z=35(7)/(8)\ in`

Explanation:

The mean of four numbers
`a,\ b,\ c, \ d` is

`(a+b+c+d)/(4)`

Given

`a=36(3)/(4)\ in\\ \\b=36(3)/(8)\ in\\ \\c=37(1)/(2)\ in\\ \\d=z\ in\\ \\\text{Mean}=36(5)/(8)\ in,`

then

`(36(3)/(4)+36(5)/(8)+37(1)/(2)+z)/(4)=36(5)/(8)`

Add numbers in the numerator:

`36(3)/(4)+36(5)/(8)+37(1)/(2)=(36+36+37)+\left((3)/(4)+(3)/(8)+(1)/(2)\right)=109+\left((6)/(8)+(3)/(8)+(4)/(8)\right)=109+(13)/(8)=109+1(5)/(8)=110(5)/(8)`

Hence,

`(110(5)/(8)+z)/(4)=36(5)/(8)\\ \\110(5)/(8)+z=36(5)/(8)\cdot 4\\ \\110(5)/(8)+z=144+(5)/(2)\\ \\110(5)/(8)+z=144+2(1)/(2)\\ \\110(5)/(8)+z=146(1)/(2)\\ \\x=146(1)/(2)-110(5)/(8)\\ \\z=146(4)/(8)-110(5)/(8)\\ \\z=36-(1)/(8)\\ \\z=35(7)/(8)\ in`