Question

Nagaraj has a​ party-length sandwich that is 45 inches long and is to be cut into three pieces. The middle piece will be 3 inches longer than the shortest​ piece, and the shortest piece will be 9 inches shorter than the longest piece. How long will the pieces​ be?

The length of the shortest piece is
_________ inches. The length of the medium piece is
_____________inches. The length of the longest piece is
__________ inches.

Answer 1

The length of the shortest piece is 11 inches. The length of the medium piece is 14 inches. The length of the longest piece is 20 inches.

Explanation:

Ok, so we have a long sandwich of 45 inches that will be divided in 3, giving us the following formula (x = shortest, y = medium, z=longest):

x + y + z = 45

Then we have middle piece (y) is 3 inches longer than the smallest (x):

y = x + 3

And the shortest piece (x) is 9 inches shorter than the longest (z):

x = z - 9 or z = x + 9

Let's place the found values of y and z in the first equation:

x + y + z = 45

x + (x + 3) + (x + 9) = 45

3x + 12 = 45

3x = 33

x = 11

So, x = 11, y = 14 and z = 20. (11 + 14 + 20 = 45).