One sheep farmer tells another farmer Give me one of your sheep and I will have the same The other farmer says Give me one of yours and I will have twice as many as you How many sheep do they have?

Answer 1

An Algebra Problem

The qualifier that their herds will be the same size with the transfer of 1 tells you there is a 2 sheep difference between the herd sizes. Farmer A has 2 less than Farmer B. The next part says that moving one sheep to the larger herd creates a 2-to-1 size ratio of the herds. With 1 more sheep, Farmer B will have 2 times Farmer A.

For the equality, if Farmer A and Farmer B loses 1 , then (A+1) = (B-1), creates the relationship B = A+2

Letting the smaller herd size be A, the larger herd is A+2.

And the transfer of 1 sheep creates the equality A+1 = (A+2)-1

The second equation says that the larger herd (presently A+2) will be twice as big as the smaller herd A if A loses 1, becoming (A-1), while the second herd becomes (A+2)+1 or A+3. This creates the formula 2(A-1) = A+3

This solves to [2A-2 = A+3] and [2A = A+5] and A = 5

The first farmer has 5 sheep, and the second farmer has 7 sheep.

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In standard algebraic form, the equations are :

[ x + 1 = y - 1 ] or y = x + 2

y+1 = 2(x-1)

Substituting, (x+2)+1 = 2(x-1) and x = 5