Question

5/8 of the 64 musicians in a music contest are guitarists. Some of the guitarists play jazz solos, and the rest play classical solos. The ratio of the number of guitarists playing jazz solos to the total number of guitarists in the contest is 1:4. How many guitarists play classical solos in the contest?

Answer 1

Now, let's start with the Guitarists:  they are 5/8 of the 64 musicians, that is


64*$\frac{5}{8} =8*5=40$

now, some number to 40 (total number of the guitarists) has the ratio of 1:4
ratios remain equivalent if we multiply both numbers by the same number.

so the ratio of 1:4 is equivalent to 10:40.

this means that there are 10 Jazz solos guitarists.

And how many classical solo guitarists were there? the rest! 40-10=30

so the answer is 30

Answer 2

If you would like to know how many guitarists play classical solos in the contest, you can calculate this using the following steps:

First, we have to find out how many musicians in a music contest are guitarists:
5/8 of 64 = 5/8 * 64 = 40 guitarists

Second, we have to divide 40 in the ratio of 1 : 4:
- add the numbers: 1 + 4 = 5
- divide and multiply: 1 / 5 * 40 = 8 ... jazz solos
                                 4 / 5 * 40 = 32 ... classical solos

Result: 32 guitarists play classical solos in the contest.