Step-by-step Solution:

Quick Solution

This puzzle can be solved by translating the statements about Ana and Andrew into a system of two algebraic equations.

1. Set Up the Equations

- Let 'g' be the total number of girls (daughters) in the family.
- Let 'b' be the total number of boys (sons) in the family.

• From Ana's perspective (as one of the girls):
  • The number of brothers she has is b.
  • The number of sisters she has is (g - 1), since we don't count Ana herself.
  The clue "has the same number of brothers as sisters" gives us our first equation:
  b = g - 1
• From Andrew's perspective (as one of the boys):
  • The number of sisters he has is g.
  • The number of brothers he has is (b - 1), since we don't count Andrew himself.
  The clue "has twice as many sisters as brothers" gives us our second equation:
  g = 2(b - 1)

2. Solve the Equations

- Now we have a system of two equations and can solve for 'g' and 'b'. Let's substitute the first equation (b = g - 1) into the second one:
g = 2( (g - 1) - 1 )
g = 2(g - 2)
g = 2g - 4
g = 4. (So, there are 4 girls).

- Now we can use the value of g to find b using the first equation:
b = g - 1
b = 4 - 1 = 3. (So, there are 3 boys).

3. Find the Total Number of Children

- The total number of children is the sum of the boys and girls.
Total Children = b + g = 3 + 4 = 7.

Final Answer: Emma has 7 children.