If Quan had 15 and Kaden had 3 times as much, then Kaden had 15(3) = 45. If he spent 10 then he had 35 left. The amount of money Quan had after his mom gave him some was 4/5 the amount of Kaden's 35 (let x = the amount of money Quan has after his mom gives him some):
35 divides by the 5 in the denominator 7 times, and 7 times 4 is 28. That's how you get your 28 in part a.
For part b., he started with 15 and ended with 28, so his mom gave him 28-15=13. That's how you get the 13.