Question

In the band there are twice as many tubas as French horns and three more trumpets than tubas. Five times the number of trumpets equals nine times the number of French horns, plus triple the number of tubas. How many of each kind of instrument are there?

Answer 1

3 French horns

6 tubas

9 trumpets

Explanation:

Let the number of French horns be x.

Number of French horns = x

There are twice as many tubas as French horns, so

Number of tubas = 2x

There are three more trumpets than tubas, so

Number of trumpets = 2x + 3

Five times the number of trumpets equals nine times the number of French horns, plus triple the number of tubas, so

`5(2x+3)=9x+3\cdot 2x\\ \\10x+15=9x+6x\\ \\10x+15=15x\\ \\15=15x-10x\\ \\15=5x\\ \\x=3\\ \\2x=6\\ \\2x+3=6+3=9`