Wanted- maths genius

Chr1s

Starting to look a bit of a plank as I can't help my daughter with her maths homework If anyone can work it out and show workings I'd be extremely grateful, Thanks In advance

Patrick had 2/3 as many stickers as Quincy. After Patrick bought another 8 stickers and Quincy lost 5 stickers, Patrick then had 4/5 as many stickers as Quincy. Find the total number of stickers Patrick and Quincy had at first.

N4T

Patrick 60 and Quincy 90

P + 8 = X And. Q - 5 = Y

Where P=2Q/3. And X=4Y/5

Substituting gives 2Q/3 + 8. = 4Y/5
Change denominator so it's the same for all ........ (10Q + 120)/15 = 12Y/15

X both sides by 15 and sub Y= Q-5........................ 150Q + 1800 = 180 (Q-5)

Do some maths here and eventually you'll get..........2700 = 180Q - 150Q
Therefore................................................................... Q = 90

and ..............................................................................P = 2x90/3 = 60