Answer:
5 trumpet players
Step-by-step explanation:
Given there are 10 fewer trumpet players than saxophone players, and the number of saxophone players is 3 times the number of trumpet players, you want to know the number of trumpet players.
Setup
Let t represent the number of trumpet players. Then 3t is the number of saxophone players, and the difference in numbers is ...
3t -t = 10
Solution
Collect terms and divide by the coefficient of t:
2t = 10
t = 5
There are 5 trumpet players.
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Additional comment
Check: There are 3 times as many sax players, so 15 of those. That's 10 more than the number of trumpet players.
You could have written the equation as ...
t +10 = 3t . . . . . . 10 more than the number of trumpets
Sometimes, when ratios are given:
t : s = 1 : 3
you can think in terms of "ratio units." Here, the difference is 3-1 = 2 ratio units, corresponding to a difference of 10 players. Then the multiplier of the ratio is 10/2 = 5:
t : s = 1 : 3 = 5 : 15 . . . . . . 5 trumpets and 15 saxophones.
