Solve for Missing Quantity: Maintaining 5:2 Ratio in Bakery Sales

To solve the problem, we'll follow these steps:

• Step 1: Identify and apply the change in quantities based on sales.
• Step 2: Set up an equation from the ratio and solve for bread.
• Step 3: Calculate how much bread was sold.

Step 1:
At the beginning, there are 50 cakes in the bakery. After selling 10 cakes, the remaining cakes are $50 - 10 = 40$.

Step 2:
At the end of the day, the ratio of bread to cakes remains 5:2. So for every 2 cakes, there are 5 loaves of bread.

If $C$ denotes the number of cakes after sales (which is 40), the number of bread $B$ is calculated based on the initial ratio:
$\frac{B}{40} = \frac{5}{2}$
Cross-multiplying gives:
$B = 40 \times \frac{5}{2} = 100$

Step 3:
Initially, the number of cakes was 50 in correspondence to the same ratio, so initially:\)
$\frac{b}{50} = \frac{5}{2}$
Solving: $b = 50 \times \frac{5}{2} = 125$

Thus, initially, there were 125 loaves of bread. At the end, there are 100 loaves, therefore the bread sold is:
$125 - 100 = 25$

Therefore, the solution to the problem is $25$.