farmer and his sheep

A farmer has three sheep. The combined weight of the sheep is 152 pounds, the smallest sheep weighs 7 pounds less the the middle-size sheep, and the largest sheep weighs 3 times the weight of the smallest sheep. What is the weight of each sheep?

Smallest = Middle - 7
Smallest = Largest / 3 'Derived by dividing by 3
Smallest + Middle + Largest = 152

This is, unfortunately, a system of 3 equations in 3 variables, so you have to reduce to one variable, find it, plug it in to get the 2nd variable, and plug both of those in to get the third variable.

Smallest = Middle - 7
Smallest = Largest / 3
(Subtract)
0 = Middle - 7 - Largest / 3

Smallest = Largest / 3
Smallest + Middle + Largest = 152
(subtract)
Middle + Largest = -Largest / 3 + 152 (multiplied by -1)
Middle + 4/3 * Largest = 152

Middle = 7 + Largest / 3
Middle = 152 - 4/3 * Largest
(subtract)
0 = -145 + 5/3 * Largest
145 = 5/3 * Largest

So, using the last equation you get
Largest = 87 (pounds)

Smallest = 87 / 3;
Smallest = 29 pounds

Smallest + 7 = Middle;
Middle = 36 pounds

Uhm... an easier representation of the same : :D

S=smallest
M= Medium
L = Largest

S+M+Z = 152

Given: S=M-7 ---> M=S+7
Given: L = 3S

Replace it,

S + S + 7 + 3S = 152
5S = 145
S = 29.

Do the rest. Short and sweet.

I just typed in into my ti-92, no bother redoing the math. ;)

Good job, jemidiah. :)

Lucky farmer!

Quote:

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Originally posted by dolor
A farmer has three sheep. The combined weight of the sheep is 152 pounds, the smallest sheep weighs 7 pounds less the the middle-size sheep, and the largest sheep weighs 3 times the weight of the smallest sheep. What is the weight of each sheep?

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The real question is...

which sheep is sexiest?

:lol:

x=small sheep
152=x+(x+7)+(3x)
152 = 5x + 7
5x = 145
x = 29

small = 29
mid = 36
large = 29*3 = 60 + 9*3 = 60+27 = 87