Answer :
To solve this problem, we need to convert the sentence into an algebraic equation and then solve for the variable [tex]\( u \)[/tex].
The sentence given is: "116 less than the product of [tex]\( u \)[/tex] and 344 is 321."
Here’s how we can break it down:
1. Identify the product of [tex]\( u \)[/tex] and 344: This is represented by [tex]\( 344u \)[/tex].
2. 116 less than the product: This means we subtract 116 from [tex]\( 344u \)[/tex], which gives us the expression [tex]\( 344u - 116 \)[/tex].
3. This expression is equal to 321: So, we set the expression equal to 321. Hence, we have the equation:
[tex]\[
344u - 116 = 321
\][/tex]
4. Solve for [tex]\( u \)[/tex]:
- Add 116 to both sides of the equation to isolate the term with [tex]\( u \)[/tex]:
[tex]\[
344u = 321 + 116
\][/tex]
- Simplify the right side:
[tex]\[
344u = 437
\][/tex]
- Divide both sides by 344 to solve for [tex]\( u \)[/tex]:
[tex]\[
u = \frac{437}{344}
\][/tex]
- This fraction is the solution for [tex]\( u \)[/tex].
Therefore, the equation derived from the sentence is [tex]\( 344u - 116 = 321 \)[/tex], and solving it gives us [tex]\( u = \frac{437}{344} \)[/tex].
The sentence given is: "116 less than the product of [tex]\( u \)[/tex] and 344 is 321."
Here’s how we can break it down:
1. Identify the product of [tex]\( u \)[/tex] and 344: This is represented by [tex]\( 344u \)[/tex].
2. 116 less than the product: This means we subtract 116 from [tex]\( 344u \)[/tex], which gives us the expression [tex]\( 344u - 116 \)[/tex].
3. This expression is equal to 321: So, we set the expression equal to 321. Hence, we have the equation:
[tex]\[
344u - 116 = 321
\][/tex]
4. Solve for [tex]\( u \)[/tex]:
- Add 116 to both sides of the equation to isolate the term with [tex]\( u \)[/tex]:
[tex]\[
344u = 321 + 116
\][/tex]
- Simplify the right side:
[tex]\[
344u = 437
\][/tex]
- Divide both sides by 344 to solve for [tex]\( u \)[/tex]:
[tex]\[
u = \frac{437}{344}
\][/tex]
- This fraction is the solution for [tex]\( u \)[/tex].
Therefore, the equation derived from the sentence is [tex]\( 344u - 116 = 321 \)[/tex], and solving it gives us [tex]\( u = \frac{437}{344} \)[/tex].
