Question

So um yeah this is a word problem for Honors Algebra and I can’t figure it out so maybe you can. It’s equations and inequalities but word form. So yeah good luck!! It’s number 4.

Answer 1

5 trumpet players

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.