Question

There are 168 members in an orchestra, and 3/8
of them play the violin. If each non-violin member practices 40 hours each week, how many hours do all of the violinists practice if they only practice2/5
of the amount of time?(3 points)
Step 1: Determine how members play the violin.

violinists

Step 2: Determine how much time each violinist spends practicing each week.

hours

Step 3: Use the answers from steps 1 & 2 to determine the total time spent practicing by all violinists.

hours

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Answer 1

Let's solve the problem step by step.

### Step 1: Determine how many members play the violin.

We know that there are 168 members in the orchestra and that \( \frac{3}{8} \) of them play the violin.

\[
\text{Number of violinists} = \frac{3}{8} \times 168
\]

Calculating this:

\[
\text{Number of violinists} = \frac{3 \times 168}{8} = \frac{504}{8} = 63
\]

So, there are **63 violinists**.

### Step 2: Determine how much time each violinist spends practicing each week.

We know that each non-violin member practices 40 hours each week. First, we determine how many non-violin members there are.

\[
\text{Number of non-violin members} = 168 - 63 = 105
\]

Now we calculate the total time spent practicing by non-violin members:

\[
\text{Total time for non-violin members} = 105 \times 40 = 4200 \text{ hours}
\]

Since violinists practice \( \frac{2}{5} \) of the amount of time that non-violin members practice:

\[
\text{Time each violinist practices} = \frac{2}{5} \times 40 = \frac{80}{5} = 16 \text{ hours}
\]

So, each violinist practices **16 hours** each week.

### Step 3: Use the answers from steps 1 & 2 to determine the total time spent practicing by all violinists.

Now we multiply the number of violinists by the time each one practices:

\[
\text{Total time for all violinists} = 63 \times 16
\]

Calculating this:

\[
\text{Total time for all violinists} = 1008 \text{ hours}
\]

Therefore, the total time spent practicing by all violinists is **1008 hours**.