If each child is given 10 sweets, there are 3 sweets left over. But if each is given 11, then the number of sweets is 4 less. Find the number of sweets.

To solve this problem, we can use a simple algebraic equation by letting $x$ represent the number of children.Step-by-Step Solution1. Create expressions for the total number of sweets:Scenario 1: If each child ($x$) gets 10 sweets, there are 3 left over.$$\text{Total Sweets} = 10x + 3$$Scenario 2: If each child gets 11 sweets, they are 4 sweets short (4 less).$$\text{Total Sweets} = 11x - 4$$2. Set the two expressions equal to each other:Since the total number of sweets remains the same in both cases:$$10x + 3 = 11x - 4$$3. Solve for $x$ (the number of children):Subtract $10x$ from both sides:$$3 = x - 4$$Add 4 to both sides:$$x = 7$$So, there are 7 children.4. Find the total number of sweets:Plug the value of $x$ back into either expression:$$\text{Total Sweets} = 10(7) + 3 = 70 + 3 = \mathbf{73}$$(Verification using the second scenario: $11(7) - 4 = 77 - 4 = 73$. The answer is consistent.)