The sum of a number and quarter of the number is 15. What is the number

Let's denote the unknown number as \( x \).

The problem states that the sum of the number and a quarter of the number is 15. This can be written as the equation:

\[
x + \frac{1}{4}x = 15
\]

To solve for \( x \), we first combine the terms on the left side:

\[
x + \frac{1}{4}x = \frac{4}{4}x + \frac{1}{4}x = \frac{5}{4}x
\]

So the equation becomes:

\[
\frac{5}{4}x = 15
\]

Now, solve for \( x \) by multiplying both sides by the reciprocal of \( \frac{5}{4} \), which is \( \frac{4}{5} \):

\[
x = 15 \times \frac{4}{5}
\]

\[
x = 3 \times 4 = 12
\]

So, the number is \( \boxed{12} \).

Would you like any details or have any questions about this solution? Here are 5 related questions you might find interesting:

1. What is the sum of a number and half of the number if the sum is 18?
2. How would you solve for \( x \) if the equation was \( x + \frac{1}{3}x = 20 \)?
3. What happens to the solution if we change the fraction to \( \frac{1}{2}x \)?
4. Can you express \( x \) in terms of a different variable if the equation was \( x + \frac{1}{n}x = 15 \)?
5. What would the equation look like if we wanted to find a number such that twice the number plus a third of the number equals 30?

**Tip:** When dealing with equations that involve fractions of a variable, it’s helpful to first combine like terms before solving.

The sum of a number and quarter of the number is 15. What is the number?

Learn how to solve an algebraic equation where the sum of a number and a quarter of that number equals 15. This problem introduces basic algebra concepts and involves combining like terms. Suitable for students in Grades 6-8.

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