A number d is equal to three times the sum of two numbers e and f

To express the relationship between the numbers \(d\), \(e\), and \(f\) given in the problem statement, we translate the sentence into a mathematical equation.

The problem states:

"A number \(d\) is equal to three times the sum of two numbers \(e\) and \(f\)."

Mathematically, this can be written as:

\[
d = 3 \times (e + f)
\]

or more simply:

\[
d = 3(e + f)
\]

### Explanation:
1. **Sum of \(e\) and \(f\)**: The expression \(e + f\) represents the sum of the two numbers \(e\) and \(f\).
2. **Three times the sum**: The expression \(3(e + f)\) indicates that the sum \(e + f\) is multiplied by 3.
3. **Equal to \(d\)**: The whole expression is equal to \(d\).

This equation represents the relationship described in the problem. 

Would you like to explore more details or have any questions about this? Here are some related questions for further practice:

1. If \(e = 4\) and \(f = 5\), what is the value of \(d\)?
2. If \(d = 30\) and \(f = 4\), what is the value of \(e\)?
3. How would the equation change if \(d\) was equal to two times the sum of \(e\) and \(f\)?
4. If \(d = 3(e + f)\), and \(e = f\), how would you express \(d\) in terms of \(e\) only?
5. If \(d = 3(e + f)\) and \(d = 18\), what are possible values for \(e\) and \(f\)?

**Tip:** Always remember to distribute multiplication over addition when solving equations involving sums and products.

Explore a mathematical problem involving a relationship between numbers, expressed through multiplication and addition in algebra. Learn how to formulate and solve equations of this type with detailed explanations and examples. Suitable for Grades 7-9.

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