There are 168 members in an orchestra, and 3/8

Question

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.