Grandmother's 2850

There were chickens and kittens in the grandmother's yard. Juraj found that if she added one more kitten, the number of kittens and chickens would be the same. But if she added five chickens to the original number, the kittens and chickens would have the same number of legs.
How many kittens does my grandmother have, and how many chickens does she have?

Correct answer:

k =  7
m =  6

Step-by-step explanation:

m+1=k
2(k+5) = 4m

m+1=k
2·(k+5) = 4·m

k-m = 1
2k-4m = -10

Pivot: Row 1 ↔ Row 2
2k-4m = -10
k-m = 1

Row 2 - 1/2 · Row 1 → Row 2
2k-4m = -10
m = 6


m = 6/1 = 6
k = -10+4m/2 = -10+4 · 6/2 = 7

k = 7
m = 6

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