I need help on a word problem

Question

There are 31 fish in a fish tank. The fish are either orange or red. There are 7 more orange fish than half the number of red fish. How many fish are orange? How many are red?

Answer 1

o = Orange Fish

r = Red Fish

You know that you have 7 more Orange fish than 1/2 the number of Red fish, so write it out...

 

(7o + 1/2r) + r = 31

 

lets solve for r

 

(7o-7) + 1/2r + r = (31-7) - subtract 7 from both sides

 

1/2r+r=24

(in simple terms 1/2+2/2 since r is a whole number)

 

3/2r = 24

 

lets clean this up...

3/2r * 2/3 = 24 * 2/3

r = 48/3

r = 16

 

So if r = 16, then o = 7 + 8 (8 being 1/2 of r)

 

o = 15

 

o + r = 31 (or 15 + 16 = 31)

 

Hope this helps.