A teacher has 53 counters. After setting aside 5, the remaining amount is shared equally among 6 groups. If 𝑥 is the number in each group, which number sentence represents the situation? A. 6(𝑥+5) =53 B. 6𝑥+5=53 C. 6𝑥 =53+5 D. 𝑥+6+5=53 Handwritten evidence: Draw or describe the groups and explain how your number sentence matches them.

The number sentence that represents the situation is B. $6x+5=53$.

Explanation:

1. Total counters: The teacher starts with 53 counters.
2. Counters set aside: 5 counters are put aside. This means the number of counters remaining to be shared is $53 - 5$.
3. Remaining counters shared: These remaining counters are shared equally among 6 groups.
4. Number in each group: Let $x$ be the number of counters in each group. Since there are 6 groups, the total number of counters in these groups is $6 \times x$, or $6x$.

So, the total number of counters in the 6 groups ($6x$) plus the 5 counters that were set aside must equal the original total of 53 counters.
This can be written as:
$6x + 5 = 53$

Handwritten evidence description:

Imagine you have 53 individual counters.

• Step 1: Setting aside. You take 5 of these counters and place them in a separate pile.

  • Original total: 53 counters
  • Pile 1 (set aside): 5 counters
  • Pile 2 (remaining): $53 - 5 = 48$ counters

• Step 2: Forming groups. You then take the 48 counters from Pile 2 and distribute them equally into 6 distinct groups.

  • Group 1: $x$ counters
  • Group 2: $x$ counters
  • Group 3: $x$ counters
  • Group 4: $x$ counters
  • Group 5: $x$ counters
  • Group 6: $x$ counters
  • The total number of counters in these 6 groups is $6 \times x$, or $6x$.

• Step 3: Relating back to the total. The counters in these 6 groups ($6x$) are the ones that were not set aside. If you combine these $6x$ counters with the 5 counters that were set aside, you must get back to the original total of 53 counters.

  • Therefore, $6x + 5 = 53$.