SOLUTION: Ken had some big and small packets of flour. The amount of flour in a big packet was 4 times as much as the amount of flour in a small packet. If he repacked 2 big packets of flour

Question 1193945: Ken had some big and small packets of flour. The amount of flour in a big packet was 4 times as much as the amount of flour in a small packet. If he repacked 2 big packets of flour into small packets, he would have 16 small packets of flour altogether. If he continued to repack the remaining big packets of flour into small packets, he would have 36 packets of flour altogether.
(a) What was the total number of small packets and big packets of flour Ken had?
(b) The difference between the total amount of flour in the big packets and small packets is 10 kg. Find the amount of flour in a big packet?

Found 2 solutions by Boreal, greenestamps:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
2 L=16S
L=8S
4L=32S
he needs to have 4 other S packets to make 36 packets.
So he started with 4 L and 4 S.
-
L-S=10
L=4S
so 3S=10
S=10/3 kg
L=40/3 kg, the answer
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Let x be the amount of flour in each small packet; then 4x is the amount in each large packet.

If all the flour were put into small packets, there would be 36 packets. Therefore the total amount of flour is 36x.

The problem says that if he repacks 2 of the large packets he started with, he would have 16 small packets. Since repacking a large packet into small packets increases the number of small packets by 4, the number of small packets he currently has is 16 - 2(4) = 8.

Those 8 small packets each have x amount of flour, making a total of 8x. The total amount of flour is 36x, so the amount of flour in the big packets is 36x-8x = 28x. And since the amount of flour in each large packet is 4x, the number of large packets he has is 28x/4x = 7.

ANSWER 1: He has 8 small packets of flour and 7 large packets.

The total amount of flour in the small packets is 8(x) = 8x; the total amount in the large packets is 7(4x) = 28x. The difference between the amounts in the large packets and the large packets is 28x-8x = 20x.

We are told that that difference is 10kg; so 20x = 10kg --> x = (1/2)kg.

So the amount of flour in each small packet is x = 1/2kg; the amount in each large packet is 4x = 2kg.

ANSWER 2: There are 2kg of flour in each large packet.

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