Answer:
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
