The ratio of two numbers is $2:3$. when 6 is subtracted from the smaller of the two numbers and 7 is added to the larger of the two, the new ratio is $2:7$. what was the smaller of the two numbers before 6 was subtracted from it

Answer:   14Step-by-step explanation:Let the smaller and larger numbers be represented by S and L, respectively.   S/L = 2/3 . . . . the original ratio of the numbers   3S = 2L . . . . . multiply by 3L__   (S-6)/(L+7) = 2/7 . . . . the new ratio of the numbers   7(S-6) = 2(L+7) . . . . . multiply by 7(L+7)   7S -42 = 2L +14Using the expression for 2L from the first ratio, we can substitute to get ...   7S -42 = 3S +14 . . . . substitute 3S for 2L   4S = 56 . . . . . . . . . . .add 42-3S   S = 14 . . . . . . . . . . . . . divide by 4The original smaller number was 14.