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Grades 9-10 Video Solutions 2013
Level 9&10 Video Solutions 2013 problem4
Level 9&10 Video Solutions 2013 problem4
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Video Transcription
Question number four, three of the numbers 2, 4, 16, 25, 50, and 125 have a product of 1,000. What is the sum of those three numbers? Certainly 1,000 can be factored in several different ways. So let's look at the prime factorization. We have 1,000 is 10 to the third, 2 to the third times 5 to the third. And let's just write that out completely. And now we see that using 25 is a possibility, but if we do that, we're stuck with three 2's, a 25 and a 5, and there is no way to use those first four numbers to make factors that are on our list. So then we can't make a 10 appear, because that's not a number on our list. Multiplying by 2 again would give us a 20, which is not on our list. So the only thing we can do is multiply the 5 with the 25 to give us a 125, and then we have no choice but to combine the 2's into a 2 and a 4. So that's the only way we can factor 1,000 given the numbers in our list, and the sum here would be 131. So that is our answer here, C to number 4.
Video Summary
Question number four, three of the numbers 2, 4, 16, 25, 50, and 125 have a product of 1,000. What is the sum of those three numbers? Certainly 1,000 can be factored in several different ways. So let's look at the prime factorization. We have 1,000 is 10 to the third, 2 to the third times 5 to the third. And let's just write that out completely. And now we see that using 25 is a possibility, but if we do that, we're stuck with three 2's, a 25 and a 5, and there is no way to use those first four numbers to make factors that are on our list. So then we can't make a 10 appear, because that's not a number on our list. Multiplying by 2 again would give us a 20, which is not on our list. So the only thing we can do is multiply the 5 with the 25 to give us a 125, and then we have no choice but to combine the 2's into a 2 and a 4. So that's the only way we can factor 1,000 given the numbers in our list, and the sum here would be 131. So that is our answer here, C to number 4.
Keywords
prime factorization
product
sum
numbers
1,000
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