Solving the Family Math Puzzle

This problem involves figuring out the number of boys and girls in a family based on clues about their siblings. We can solve this using algebra.

Setting Up the Variables

Let's define:

• B = the total number of boys in the family.
• G = the total number of girls in the family.

Analyzing the Clues

We are given two main conditions:

1. From a boy's perspective: "Each boy in this family has as many sisters as brothers."
   • When a boy counts his siblings, he doesn't count himself.
   • Number of brothers he has = B - 1
   • Number of sisters he has = G
   • So, the equation is: B - 1 = G
2. From a girl's perspective: "each girl has twice as many brothers as sisters."
   • When a girl counts her siblings, she doesn't count herself.
   • Number of brothers she has = B
   • Number of sisters she has = G - 1
   • So, the equation is: B = 2 * (G - 1)

Solving the Equations

Now we have a system of two equations:

1. G = B - 1
2. B = 2(G - 1)

We can use substitution to solve for B and G. Let's substitute the first equation into the second one:

Substitute G from equation (1) into equation (2):

B = 2((B - 1) - 1)

Simplify the expression inside the parentheses:

B = 2(B - 2)

Distribute the 2:

B = 2B - 4

To solve for B, let's rearrange the equation:

Subtract B from both sides:

0 = B - 4

Add 4 to both sides:

B = 4

So, there are 4 boys in the family.

Now, let's find the number of girls using the first equation (G = B - 1):

G = 4 - 1

G = 3

So, there are 3 girls in the family.

Verifying the Solution

Let's check if our numbers (4 boys, 3 girls) satisfy the original conditions:

• Check condition 1 (Boy's perspective): A boy has 4 - 1 = 3 brothers and 3 sisters. Does he have as many sisters as brothers? Yes, 3 = 3.
• Check condition 2 (Girl's perspective): A girl has 4 brothers and 3 - 1 = 2 sisters. Does she have twice as many brothers as sisters? Yes, 4 = 2 * 2.

Both conditions are met.

Final Answer

The family has 4 boys (brothers) and 3 girls (sisters).