Francisco is the youngest of four siblings whose ages are consecutive integers. If the sum of their ages is 74, find Francisco's age.

Let Francisco's age be represented by \( x \). Since Francisco is the youngest of four siblings, the ages of the siblings are consecutive integers, so their ages can be expressed as:

- Francisco: \( x \)
- Second sibling: \( x + 1 \)
- Third sibling: \( x + 2 \)
- Fourth sibling: \( x + 3 \)

The sum of their ages is given as 74, so we can set up the following equation:

\[
x + (x + 1) + (x + 2) + (x + 3) = 74
\]

Simplifying the left-hand side:

\[
4x + 6 = 74
\]

Subtract 6 from both sides:

\[
4x = 68
\]

Now divide by 4:

\[
x = 17
\]

Thus, Francisco's age is \( \boxed{17} \).

Would you like more details or have any questions?

Here are 5 related questions for you to consider:
1. What would the siblings' ages be if the sum was 80 instead of 74?
2. If the sum of their ages was reduced by 10, what would Francisco’s age be?
3. Can you find a general formula for Francisco's age if the total age sum is \( S \)?
4. How would the solution change if the siblings’ ages were not consecutive integers?
5. If each sibling’s age is doubled, what would their new age sum be?

**Tip**: For consecutive numbers, equations often simplify into terms involving multiples of the smallest number!

Solve a problem where Francisco is the youngest of four siblings with consecutive ages, and their total sum is 74. This step-by-step solution involves algebraic equations and the concept of consecutive integers, suitable for students in Grades 6-8.

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