Vincen 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) = G
We now have the following system:
B = G-1
2(B-1) = G
Simplify the bottom equation to get:
B = G - 1
2B - 2 = G
Take 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)
Cheers,
Brent
