i need help on this ratio please i dont understand it thanks

Question

a fruit basket contained apples and oranges in the ratio of 5:4. after joe ate one of the apples the ratio was 6:5. how many oranges are in the basket?

Answer 1

a=# of apples

r=# of oranges

a/r=5/4

a-1/r=6/5

cross multiply with both equations

4a=5r

5(a-1)=6r

5a-5=6r

from 4a=5r we get a=(5/4)r

substitute

5(5/4)r-5=6r

(25/4)r-5=6r

(6 1/4)r-6r=5

(1/4)r=5

r=20 oranges

a/20=5/4

5*4=20 so 5*5=25 apples, or cross multiply...

4a=5*20

4a=100

a=25 apples

25/20=5/4

(25-1)/20=24/20=6/5

using just arithmetic...

5+4=9 and 6+5=11

you want a number that is a multiple of 9 and that number becomes a multiple of 11 when 1 is subtracted from the total

9,18,27,36,45 stop !!

45-1=44 which is a multiple of 11

45/9=5 and 5*5=25 and 5*4=20