If we name "k" the amount of apples that Kayla has, and "r" the amount of apples thata Richard has, we know that r + k =48 (the two of them together have 48 apples).
In addition, we know that Kayla has 35% more apples than Richard. This means that k (1-0.35) = r (the apples of Richard are 0.35 % smaller than the apples of Kayla). Then 0.65 k = r
Then, taking these two considerations together, r + k= 48 and 0.65 k= r, imply 0.65 k + k = 48 (I just replace the second equation into the first one). Which finally means that k= 29 (and r = 19 because r+ k=48).
If Kayla has 162 apples, and according previous statements, she has 35% more apples than Richard, this means that 0.65 k= r, therfore if k=162, r= 162 x 0.65 = 105 (Richar has 105 apples).
