Sure! Let's go step-by-step to translate the given sentence into a mathematical equation.
1. Understanding the phrase:
- "Six more than": This indicates that we are adding 6 to some other quantity.
- "the quotient of a number and 2": This means we are dividing the unknown number by 2.
2. Introducing the variable [tex]\( w \)[/tex]:
- Let [tex]\( w \)[/tex] represent the unknown number.
3. Constructing the expression:
- "the quotient of a number and 2" translates to [tex]\( \frac{w}{2} \)[/tex].
- "Six more than" translates to adding 6 to this quotient.
4. Forming the entire sentence:
- Combining these parts, "Six more than the quotient of a number and 2 is 8" translates to:
[tex]\[
\frac{w}{2} + 6 = 8
\][/tex]
5. Setting up the equation:
- We have the final equation:
[tex]\[
\frac{w}{2} + 6 = 8
\][/tex]
So, the equation that represents the sentence "Six more than the quotient of a number and 2 is 8" is:
[tex]\[
\frac{w}{2} + 6 = 8
\][/tex]
