Let x be the total number of students.
We know that 7/8x chose music over art.
5/7 of those students want to learn an instrument, so we have to multiply the number of students who chose music by 5/7:
[tex]\dfrac{7x}{8}\cdot \dfrac{5}{7}=\dfrac{5x}{8}[/tex]
So, 5/8 of the students want to learn an instrument.