We are given that 146 musicians are seated in rows of 15. a. We need to find the number of rows of seats needed. b. If as many rows are filled as possible, we need to find the number of musicians in the row that is not full.

1. Problem Description

We are given that 146 musicians are seated in rows of

1

5. a. We need to find the number of rows of seats needed.

b. If as many rows are filled as possible, we need to find the number of musicians in the row that is not full.

2. Solution Steps

a. To find the number of rows needed, we divide the total number of musicians by the number of musicians per row. Since we cannot have a fraction of a row, we need to round up to the nearest whole number.

$146 \div 15 = 9.7333...$

Since we can't have a fraction of a row, we round up to the nearest whole number, which is

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0. Therefore, 10 rows are needed.

b. To find the number of musicians in the row that is not full, we first find the number of full rows. The number of full rows is the integer part of $146 \div 15$, which is

9. Then we multiply the number of full rows by the number of musicians per row to find the number of musicians in the full rows. Finally, we subtract the number of musicians in the full rows from the total number of musicians to find the number of musicians in the row that is not full.

Number of full rows = $\lfloor 146 \div 15 \rfloor = 9$

Number of musicians in full rows = $9 \times 15 = 135$

Number of musicians in the row that is not full = $146 - 135 = 11$

3. Final Answer

a. 10

b. 11