The ratio of the number of apples Nicole and Hannah had was 1:3. When Nicole bought 4 more apple and Hannah bought 3 more apples, the ratios became 1:2. Find the number of applles Hannah had in the end.
+129847 N / H = 1 / 3 ⇒ N = (1/3)H (1)
And
( N + 4) / ( H + 3) = 1 / 2 (2)
Sub (1) into (2) for N
[ (1/3)H + 4 ] / ( H + 3 ) = 1 / 2 cross-multiply
2 [ (1/3) H + 4 ] = H + 3
(2/3)H + 8 = H + 3
8 - 3 = H - (2/3) H
5 = (1/3) H
H = 5 (3/1) = 15
In the end Hannah had H + 3 = 18 apples
+1694 N : H = 1 : 3
(x + 4) / (3x + 3) = 1/2
x = 5
Hannah had 3*5+3 = 18 apples 
