Sure, let's interpret the given situation step-by-step and translate it into a mathematical equation.
1. Situation Breakdown:
- Each of the [tex]\( s \)[/tex] students gets 15 pieces of candy.
- The total number of pieces of candy in the bag is 310.
- There are 10 pieces of candy remaining after distribution.
2. Calculate Total Pieces Given Away:
Each student gets 15 pieces of candy. So, for [tex]\( s \)[/tex] students:
[tex]\[
\text{Total pieces given away} = s \times 15
\][/tex]
3. Express Total Pieces in the Bag:
The bag originally contains 310 pieces of candy. After [tex]\( s \)[/tex] students get their pieces and 10 pieces remain:
[tex]\[
\text{Total pieces given away} + \text{pieces remaining} = \text{total pieces in the bag}
\][/tex]
Thus,
[tex]\[
(s \times 15) + 10 = 310
\][/tex]
4. Simplify the Expression:
To find the correct equation, isolate [tex]\( s \)[/tex]:
[tex]\[
s \times 15 = 310 - 10
\][/tex]
[tex]\[
s \times 15 = 300
\][/tex]
However, this isn't quite the same as any of the given options. Let's evaluate each option to see if any closely matches or logically represents the situation described:
- [tex]\(( s \times 15) \div 10 = 310\)[/tex]: This suggests that [tex]\(s \times 15\)[/tex] pieces divided by 10 equals 310, which does not correctly describe the scenario.
- [tex]\(( s +15) = 310 + 10\)[/tex]: This suggests that the number of students plus 15 equals 320, which is incorrect.
- [tex]\((310-10) +15 = s \)[/tex]: This rearrangement still does not logically fit the context.
- [tex]\(310 \div(s+15) = 10\)[/tex]: This suggests dividing 310 by the sum of students and 15 equals 10, which does not suit the distribution summary.
Given the options, none directly represent the steps and analysis above correctly. However, let's represent the situation correctly:
[tex]\[
(s \times 15) + 10 = 310
\][/tex]
By isolating [tex]\(s\)[/tex], you would eventually solve
[tex]\[
s \times 15 = 300
\][/tex]
So, unfortunately, none of the provided multiple choices correctly describe the original context without rearrangement misinterpretation.
Therefore, we can conclude with certainty that none of the given equations adequately represent the situation accurately.
However, based on the logical sequence, the most appropriate approach confirms none precisely fit:
```
None of the given equations accurately represent the initial detailed description considering candy distribution to students explicitly.
```
