Nagaraj has a party-length sandwich that is 55 inches long and is to be cut into three pieces. the middle piece will be 4 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?

S = 14 inches

M = 18 inches

L = 23 inches

Step-by-step explanation:

Let's being by defining our variables:

Shortest piece = S

Middle piece = M

Longest piece = L

So now we need to write down what formulas we're given:

"Nagaraj has a party-length sandwich that is 55 inches long and is to be cut into three pieces"

so we can start by knowing the S + M + L = 55

"The middle piece will be 4 inches longer than the shortest piece"

This means that M - 4 = S

"the shortest piece will be 9 inches shorter than the longest piece"

Finally, this means that S + 9 = L

What we need to do now is turn all of these things into the form of one letter. We can see that S is in all three of these equations, so lets solve everything in terms of S.

M = S + 4

L = S + 9

Now we can plug in both of those things into our first equation to get:

S + S + 4 + S + 9 = 55

and now we solve :)

3S = 42

S = 14

So now given this we can use this to solve the other three lengths

M = 14 + 4 = 18

L = 14 + 9 = 23