a nd b each have a certain number of mangoes

Question

a and b both have a certain number of mangoes. a says to b" if you give 30 of your mangoes, i will have twice as many as left with you." b replies"if you give me 10, i will have thrice as many as left with you." how many mangoes does each have?

Answer 1

Let a and b also represent the amounts each has at the beginning.

a+30=2(b-30); a+30=2b-60; a-2b=-90 or -a+2b=90.

b+10=3(a-10)=3a-30; 3a-b=40; 6a-2b=80.

-a+6a=170; 5a=170, a=34. 2b=90+a=124, b=62.

CHECK: b gives a 30 mangoes, so a now has 64 mangoes and b has 32. 64=2*32.

a gives b 10 mangoes, so b now has 72 mangoes and a has 24. 72=3*24.