DensetsuNo wrote:

Ana is a girl and has the same number of brothers as sisters. Andrew is a boy and has twice as many sisters as brothers. Ana and Andrew are the children of Emma. How many children does Emma have?

(A) 2

(B) 3

(C) 5

(D) 7

(E) 8

Let B = number of boys that Emma has

Let G = number of girls that Emma has

Ana is a girl and has the same number of brothers as sisters. B = the number of brothers Ana has

Since Ana is one of Emma's girls, we know that G-1 = the number of sisters Ana has (we cannot include Ana in this count, since Ana is not her own sister)

We can write:

B = G-1 Andrew is a boy and has twice as many sisters as brothers. G = the number of sisters Andrew has

Since Andrew is one of Emma's boys, we know that B-1 = the number of brothers Andrew has

We can write:

2(B-1) = GWe now have the following system:

B = G-12(B-1) = GSimplify the bottom equation to get:

B = G - 12B - 2 = GTake the

blue equation and replace B with G-1 to get: 2(G-1) - 2 = G

Expand: 2G - 2 - 2 = G

Solve: G = 4

When we plug G = 4 into either equation and solve for B, we get B = 3

So, B+G = 3+4 = 7

So, Emma has 7 children (3 boys and 4 girls)

Answer:

Cheers,

Brent

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