Question

A 90-inch length of ribbon is to be cut into three pieces. The longest piece is to be 30 inches longer than the shortest piece, and the third piece is to be half the length of the longest piece. Find the length of each piece of ribbon.

Answer 1

Lets name the shortest piece a, the medium b and the longest c

Together they are 90inches
$a + b + c = 90$
The longest is 30 inches longer than the shortest
$c = a + 30$
The third piece is half the lenght of the longest
$b = \frac{c}{2}$

So if you place c=a+30 in the other 2 equasions you get

$a + b + (a + 30) = 90 = 2a + b + 30$
And
$b = \frac{30 + a}{2}$
Now if you put this 2 toghether u get
$2a + \frac{30 + a}{2} + 30 = 90$
Multyplied by 2
$4a + 30 + a + 60 = 180$
$5a = 90$
Meaning that a=18inches

Now that we have the lenght of a we put it in the previous equasion

$b = \frac{30 + 18}{2}$
So b=48/2 which means b=24inches

And together they must be 90 so

$18 + 24 + c = 90$

C=48inches