Agus sold packets of sweets to Halim and Kairi in the ratio 8:13.He sold the sweets in 2-kg packets.What was the smallest possible mass of sweets Agus sold to both of them?
2(8+13)=42
Ah, the age-old question of sweets and ratios. Well, if Agus sold the sweets in a ratio of 8:13, we can assume that the total number of parts is 8 + 13 = 21.
Now, if each part represents a 2-kg packet of sweets, we can find the smallest possible mass by dividing the total mass in packets (21 * 2 kg) by the total number of parts.
So, the mass of sweets that Agus sold to both Halim and Kairi would be (21 * 2 kg) / 21 = 2 kg.
Now, that might not sound like a lot of sweets, but hey, at least they're getting something, right? Better than no sweets at all!
To find the smallest possible mass of sweets Agus sold to both Halim and Kairi, we need to determine the least common multiple (LCM) of 8 and 13.
The prime factors of 8 are 2 x 2 x 2.
The prime factors of 13 are 13.
To find the LCM, we multiply the highest power of each prime factor:
2 x 2 x 2 x 13 = 104.
So, the LCM of 8 and 13 is 104.
Since Agus sold the sweets in 2-kg packets, we divide the LCM by 2:
104 / 2 = 52.
Therefore, the smallest possible mass of sweets Agus sold to both Halim and Kairi is 52 kg.
To find the smallest possible mass of sweets Agus sold to both Halim and Kairi, we need to determine the smallest common multiple of 8 and 13. This will give us the total number of 2-kg packets sold.
The smallest common multiple of two numbers, in this case 8 and 13, can be found by using the prime factorization method. Let's factorize the two numbers:
8 = 2 × 2 × 2
13 = 13
Next, we take the highest power of each prime number:
For 2, we take the highest power which is 2^3 = 8.
For 13, we take the highest power which is 13^1 = 13.
Finally, we multiply these highest powers together:
8 × 13 = 104
To get the smallest possible mass of sweets Agus sold, we multiply the total number of packets (104) by the mass of each packet (2 kg):
104 × 2 = 208 kg
Therefore, the smallest possible mass of sweets Agus sold to both Halim and Kairi is 208 kg.