Solving the Toffee Distribution Problem

This problem requires us to find the number of toffees child B has, given information about child A's toffees and B's share relative to the total.

Setting Up the Equations

Let $A$ be the number of toffees child A has, and $B$ be the number of toffees child B has.

• We are given that child A has 8 toffees: $A = 8$.
• Child B has one toffee more than 50% of the total toffees. The total number of toffees is $A + B$. So, B's toffees can be expressed as: $B = (0.50 \times (A + B)) + 1$.

Calculating B's Toffees

Now, we substitute the known value of $A$ into the equation for $B$ and solve for $B$.

1. Substitute $A = 8$ into the equation for $B$:

   $B = (0.50 \times (8 + B)) + 1$

2. Distribute the 0.50:

   $B = (0.50 \times 8) + (0.50 \times B) + 1$

   $B = 4 + 0.5B + 1$

3. Combine the constant terms:

   $B = 5 + 0.5B$

4. Isolate the term with $B$ by subtracting $0.5B$ from both sides:

   $B - 0.5B = 5$

   $0.5B = 5$

5. Solve for $B$ by dividing both sides by 0.5:

   $B = \frac{5}{0.5}$

   $B = 10$

Conclusion

Therefore, child B has 10 toffees.