A retailer bought a bag of tea leaves. If the retailer were to repack the tea leaves into smaller packets of either 40g, 250, or 350g, determine the least mass, in grams, of the tea leaves in the bag.
40 = (2)(2)(2(5)
250 = (2)(5)(5)(5)
350 = (2)(5)(5)(5)
= (2)(2)(2)(5)(5)(5)(7)
= 7000g
is that correct
yes for the 7000, but 350 = (2)(7)(5)(5)
To determine the least mass of the tea leaves in the bag, you need to find the highest exponent of each prime factor among the three packet sizes (40g, 250g, and 350g).
For the prime factor 2:
- The highest exponent among the three packet sizes is 3.
For the prime factor 5:
- The highest exponent among the three packet sizes is 3.
For the prime factor 7:
- The highest exponent among the three packet sizes is 1.
To find the least mass, multiply the prime factors with their respective highest exponents:
2^3 * 5^3 * 7^1 = 8 * 125 * 7 = 7000g.
So, your answer of 7000g is correct.