SOLUTION: Alice has four cats. She decided to weigh them in pairs. Silly and Pitty together weighed 110 lbs. Pitty and Neta together weighed 103 lbs., and Neta and Eta toghether weighed 10

Question 44919: Alice has four cats. She decided to weigh them in pairs. Silly and Pitty together weighed 110 lbs. Pitty and Neta together weighed 103 lbs., and Neta and Eta toghether weighed 108 lbs. How many pounds would Silly and Eta weigh together?

Answer by abhijitvakil(7) (Show Source): You can put this solution on YOUR website!
We get 3 equations in four variables from the above question as below:
S + P = 110 ...... (1)
P + N = 103 ...... (2)
N + E = 108 ...... (3)
The student may observe that the question itself is an equation :
S + E = ? ..... (4)
Now, the variables S & E appear in equations nos (1) & (3) above. Hence if we add these two equations, we get a new equation as :
S + P + N + E = 110 + 108 ... (5)
From equation (2), we have P + N = 103. We substitute this value of P + N in eq (5) :
S + 103 + E = 110 + 108
or
S + E = 110 + 108 - 103 = 115
Thus Silly & Eta together weigh 115 lbs.
The trick in such type of questions is to identify variables and look for relations between them. Note down each relation as an equation. You should get as many equations as there are variables, to be able to solve them. In the problem above, we were not asked to find values of each variable, hence we had 4 variables and 3 equations. The 4th equation itself was the solution.
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