Question

Baker sam mades some mooncakes and packed them equally into boxes. He gave 2 5 of the mooncakes to QQ Home and 4 9 of the remainder to KK Hom. He had 60 boxes of mooncakes left.
(a) How many boxes of mooncakes did sam make?
(b) How many boxes of mooncaked did baker sam give to KK Home?

Answer 1

Let's assume that Baker Sam made a total of x boxes of mooncakes.
He gave 2/5 of the mooncakes to QQ Home, which is (2/5)*x = 2x/5 boxes.
So, the remainder of mooncakes is x - 2x/5 = (5x - 2x)/5 = 3x/5 boxes.
Baker Sam gave 4/9 of the remainder to KK Home, which is (4/9)*(3x/5) = (4*3x)/(9*5) = 12x/45 = 4x/15 boxes.
He had 60 boxes of mooncakes left, so 60 = (3x/5) - (4x/15).
Multiplying everything by 15 to get rid of the fractions, we get 900 = 9(3x) - 4(4x).
So, 900 = 27x - 16x.
Combining like terms, we get 900 = 11x.
Dividing both sides by 11, we get x = 900/11.
Thus, Baker Sam made x = 900/11 = 81.82 ~ <<81.82=81>>81 boxes of mooncakes.
Baker Sam gave 4x/15 = (4*81)/15 = 324/15 = 21.6 ~ 22 boxes of mooncakes to KK Home. Answer: \boxed{22}.