Question

A 36 foot long ribbon is cut into three pieces. The first piece of ribbon is half as long as the second piece of ribbon. The third piece is 1 foot longer than twice the length of the second piece of ribbon. How long is the longest piece of ribbon?

Answer 1

The longest piece is 21 feet.

Explanation:

Let the three pieces be x,y and z.

The first piece of ribbon is half as long as the second piece of ribbon.

`x= (y)/(2)` ....(1)

The third piece is 1 foot longer than twice the length of the second piece of ribbon.

`z=2y+1` .........(2)

And together all pieces measure 36 feet.

`x+y+z=36` ......(3)

Substituting values of x and z in (3)

`(y)/(2)+ y+2y+1=36`

Solving this we get;

`(y+2y+4y+2)/(2)=36`

=>
`(7y+2)/(2)=36`

=>
`7y+2=72`

=>
`7y=70`

y = 10 feet

As
`x= (y)/(2)`

`x= (10)/(2)`

x = 5 feet

And also
`x+y+z=36`

=>
`10+5+z=36`

=>
`15+z=36`

=>
`z=36-15`

z = 21 feet

Hence, the longest piece is 21 feet.

Answer 2

The third string is the longest.

a = first string
b = second string
c = third string

The first column, closest to the left, is the equations derived from the problem. Because the last two equations all have "b" in common, replace "a" and "c" in the first equation with what they equal to. (a+b+c=36 becomes [(2b) + b + (2b+1) = 36]) Then, solve for "b". Once you have found "b", plug it in the equation for the first and third string; compare.

(The reason why I only said the third string is the longest and not the length specifically, is so you can figure out the final answer completely on your own. )