Baker sam made 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 Home he had 60 of mooncakes left.

Question

(A) How many boxes of mooncakes did sam make?
(B) How many boxes of mooncakes did baker sam give to KK Home?

Answer 1

Let's solve this problem step by step.

(A) To find out how many boxes of mooncakes Sam made, we need to work backward from the number of mooncakes he had left.

First, we know that he gave away 2/5 of the mooncakes to QQ Home and 4/9 of the remainder to KK Home.

Let's assume that the number of mooncakes Sam made is "x". After giving away 2/5 of the mooncakes to QQ Home, he has (3/5)x mooncakes remaining. Then, he gives away 4/9 of this remainder to KK Home.

The number of mooncakes he gives to KK Home is (4/9)(3/5)x = (12/45)x = (4/15)x.

From the information given, we know that he had 60 mooncakes left. So, we can set up the equation as follows:

(4/15)x = 60

To solve for x, we can multiply both sides of the equation by 15/4 to isolate x:

x = (60)(15/4)
x = 225/2
x = 112.5

Since we can't have a fraction of a box, we need to round up to the nearest whole number. Therefore, Sam made 113 boxes of mooncakes.

Answer: Sam made 113 boxes of mooncakes.

(B) To find out how many boxes of mooncakes Sam gave to KK Home, we can multiply the number of boxes by (4/15).

Number of boxes given to KK Home = (4/15)(113)
Number of boxes given to KK Home = 30.07

Again, we can't have a fraction of a box, so we round up to the nearest whole number.

Answer: Sam gave 31 boxes of mooncakes to KK Home.