Students contributed some money to help needy people. They bought twenty four 2-kg packets of flour, thirty six 1-kg packets of flour and a fifty kilogram bag of sugar. The flour was packed in 500 g packets and the sugar in 250 g packets. How many people got both a packet of flour and a packet of sugar?
24*2+36 = 84 kg flour
50 kg sugar
So, now you can figure how many packets of each were made, and thus how many got both.
84/.5 = 168
50/.25 = 200
= 368
To determine the number of people who received both a packet of flour and a packet of sugar, we need to find the least common multiple (LCM) of the quantities of flour and sugar packets. The LCM will give us the number of combined packets.
First, let's calculate the number of packets for each item:
- There are 24 packets of 2 kg flour, which is equivalent to 2000 grams. Each packet has 500 grams, so we have 2000 / 500 = 4 packets.
- There are 36 packets of 1 kg flour, which is equivalent to 1000 grams. Again, each packet has 500 grams, so we have 1000 / 500 = 2 packets.
- There is a 50 kg bag of sugar, which is equivalent to 50000 grams. Each packet has 250 grams, so we have 50000 / 250 = 200 packets.
Now, let's find the LCM of the quantities: 4, 2, and 200.
The prime factorization of these numbers is:
4 = 2^2
2 = 2^1
200 = 2^3 * 5^2
To find the LCM, we take the highest powers of all the prime factors from the numbers: 2^3 * 5^2 = 8 * 25 = 200.
Therefore, the LCM of the quantities is 200 packets.
Since each packet includes both a packet of flour and a packet of sugar, the answer is 200 people received both a packet of flour and a packet of sugar.