Answer:
3 girls and 4 boys
Step-by-step explanation:
Writing the number of girls in the family as g and the number of boys in the family as b,
we know that each girl has twice as many brothers as sisters. Therefore, the amount of boys in the family (b, or how many brothers each girl has) is twice the number of the amount of girls in the family (g) minus 1 (g-1) (subtract 1 because each girl's number of sisters does not include the girl herself). We can write this as
b = 2(g-1)
Next,
we know that each boy has the same amount of brothers as sisters. Therefore, the amount of boys in the family minus 1 (b-1, subtracting 1 because we don't include the boy that has the brothers) is equal to the amount of girls in the family (g). we can write this as
b-1 = g
Therefore, we have
b = 2(g-1)
b-1 = g
Plugging b-1 = g into the first equation, we get
b = 2 (g-1)
2(g-1) = 2((b-1) - 1) = b
= 2(b-1-1)
= 2(b-2)
= 2b-4
b = 2b-4
subtract 2b from both sides to make it so that only b values and their coefficients are on one side
-b = -4
multiply both sides by -1 to solve for b
b=4
Therefore, there are 4 boys in the family and b-1 = 4-1 = 3 girls in the family.
