Once upon a time in mumbai .
Algebra
Level
3
Once upon a time in mumbai , there were some cats and rats , if each cat catches 1 rat then 1 cat is left , if 2 cats catches 1 rat then 1 rat is left . What is the sum of number of cats and rats .
9
4
5
7
10
8
6
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1 solution
c = cats r = rats
Statement 1: "If each cat catches 1 rat, there is 1 cat left." From this we get there are r rats, and r+1 cats. Therefore, c = r+1.
Statement 2: "If 2 cats catch 1 rat, there is 1 rat left." For each pair of cats, there is 1 rat. There is 1 more rat than pairs of cats (r-1 pairs of cats). From this we now know there are r rats and 2(r-1) cats. Therefore, c = 2(r-1).
c from statement 1 = c from statement 2. r+1 = 2(r-1) = 2r - 2. r = 3.
c = r+1 = 3+1 = 4.
Therefore, r + c = 3 + 4 = 7.