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

Options

A. 2
B. 3
C. 5
D. 7

Answer

Let's solve the problem step by step.

### Step 1: Define Variables
Let:
- \( b \) = number of brothers
- \( s \) = number of sisters

### Step 2: Analyze Ana's Situation
Ana is a girl and has the same number of brothers as sisters. Therefore:
- The number of brothers \( b \) is equal to the number of sisters \( s - 1 \) (since Ana is not counted as her own sister).

This gives us the equation:
\[ b = s - 1 \]

### Step 3: Analyze Andrew's Situation
Andrew is a boy and has twice as many sisters as brothers. Therefore:
- The number of sisters \( s \) is equal to twice the number of brothers \( b - 1 \) (since Andrew is not counted as his own brother).

This gives us the equation:
\[ s = 2(b - 1) \]

### Step 4: Substitute the First Equation into the Second
From the first equation, we can express \( b \) in terms of \( s \):
\[ b = s - 1 \]

Now substitute this expression for \( b \) into the second equation:
\[ s = 2((s - 1) - 1) \]
\[ s = 2(s - 2) \]
\[ s = 2s - 4 \]

### Step 5: Solve for \( s \)
Rearranging the equation gives:
\[ s - 2s = -4 \]
\[ -s = -4 \]
\[ s = 4 \]

### Step 6: Find \( b \)
Now substitute \( s = 4 \) back into the first equation to find \( b \):
\[ b = s - 1 = 4 - 1 = 3 \]

### Step 7: Calculate Total Children
The total number of children Emma has is the sum of brothers and sisters:
\[ \text{Total Children} = b + s = 3 + 4 = 7 \]

### Final Answer
Emma has **7 children**.

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