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?
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}.
(a) To find the number of boxes of mooncakes Sam made, we need to work backwards. Since he had 60 boxes left after giving some to QQ Home and KK Home, we can calculate the remaining mooncakes using reverse operations.
Let's start by finding the total number of mooncakes.
- If he gave 2/5 of the mooncakes to QQ Home, then the remainder is 3/5 (1 - 2/5 = 3/5).
- If he gave 4/9 of the remainder to KK Home, then the remaining fraction is 5/9 (1 - 4/9 = 5/9).
The number of boxes remaining (60) represents 5/9 of the total number of boxes Sam made, so we can set up the equation:
5/9 * Total Boxes = 60
To solve for the total number of boxes, we multiply both sides of the equation by 9/5:
Total Boxes = 60 * 9/5
Total Boxes = 108
Therefore, Sam made 108 boxes of mooncakes.
(b) To find the number of boxes of mooncakes Sam gave to KK Home, we multiply the total number of boxes (108) by the fraction given to KK Home (4/9).
Boxes for KK Home = 108 * 4/9
Boxes for KK Home = 48
Therefore, Sam gave 48 boxes of mooncakes to KK Home.
To find the answers to these questions, let's break down the information given step by step.
We know that baker Sam gave 2/5 of the mooncakes to QQ Home and 4/9 of the remainder to KK Home. We're also told that after these distributions, Sam had 60 boxes of mooncakes left.
(a) To find the total number of boxes Sam made, we need to work backward from the remaining 60 boxes. Since we know that 4/9 of the remainder was given to KK Home, this means that KK Home received (4/9) * (remaining mooncakes) = (4/9) * (60 boxes). Let's calculate this:
KK Home received (4/9) * (60 boxes) = (240/9) = 80/3 ≈ 26.67 boxes
But the number of boxes has to be a whole number, so let's round it down to the nearest whole number:
KK Home received 26 boxes
Now, let's find out how many mooncakes remained after KK Home received their share. Sam had 60 boxes left, and KK Home received 26 boxes. So the remaining mooncakes would be: 60 - 26 = 34 boxes.
Since 2/5 of the mooncakes were given to QQ Home, we can calculate the number of boxes QQ Home received:
QQ Home received (2/5) * (34 boxes) = (68/5) ≈ 13.6 boxes
Again, rounding this down to the nearest whole number:
QQ Home received 13 boxes
To find the total number of boxes Sam made, we add up the boxes given to KK Home, QQ Home, and the remaining boxes:
Total boxes made = Boxes given to KK Home + Boxes given to QQ Home + Remaining boxes
= 26 + 13 + 34
= 73 boxes
Therefore, Sam made a total of 73 boxes of mooncakes.
(b) We have already calculated that KK Home received 26 boxes of mooncakes.