hello pls explain well

Question

There were 476 foldable and non-foldable bicycles in a shop for sale. After 208 bicycles were sold, 5/9 of the non-foldable bicycles and 4/7 of the foldable bicycles were left in the shop. How many foldable bicycles were sold?

Answer 1

f + n = 476

n =476-f

f= 476-n

476 originally = n+f

476-208= 268 left

5n/9 + 4f/7 = 476-208=268

5(476-f)/9 + 4f/7 = 268

multiply by 7(9) to eliminate fractions

5(7)(476-f) +4(9)f = 268(7)(9)

5(7)(476) - 5(7)f + 4(9)f = 268(7)(9)

36f-35f = 268(7)(9)-476(5)(7)

f = 224 original foldable bicycles

n = 476-224 = 252 non-foldable bicycles originally

5n/9 = 5(252)/9 = 5(28)=140 non-foldables left

4f/7 = 4(224)/7 = 4(32) = 124 foldables left

224-124 = 100 foldables sold

252-140 = 112 non-foldables sold