Question

the ratio of trumpet players to trombone players in the band is 5:3. what does this mean?
a. there are 2 more trumpet players than trombone players.
b. for every 5 trombone players, there are 3 trumpet players.
c. there are 5 more trumpet players than trombone players.
d. for every 5 trumpet players, there are 3 trombone players.

Explanation:

A ratio \(a:b\) means that for every \(a\) units of one quantity, there are \(b\) units of another quantity. Here, the ratio of trumpet players to trombone players is \(5:3\). So, for every \(5\) trumpet players, there are \(3\) trombone players.

• Option A: Just knowing the ratio \(5:3\) doesn't tell us the difference in the number of players. For example, if there are \(5\) trumpet and \(3\) trombone players, the difference is \(2\), but if there are \(10\) trumpet and \(6\) trombone players (since \(10:6 = 5:3\)), the difference is \(4\). So, this option is wrong.
• Option B: The ratio is trumpet : trombone \(=5:3\), not trombone : trumpet \(=5:3\). So, this option is wrong.
• Option C: Similar to option A, the ratio \(5:3\) doesn't give the exact difference in the number of players. So, this option is wrong.
• Option D: This correctly interprets the ratio \(5:3\) (trumpet : trombone) as for every \(5\) trumpet players, there are \(3\) trombone players.

Answer:

D. For every 5 trumpet players, there are 3 trombone players.