# Why is this the answer

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#1
The question is Find the largest three consecutive even numbers that sum to less than 1000. The answer is 330,332 & 334 but why is this the answer. To me it makes no sense.
Last edited by Aa008; 2 years ago
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2 years ago
#2
(Original post by Aa008)
The question is Find the largest three consecutive even numbers that sum to less than 1000. The answer is 330,332 & 334 but why is this the answer. To me it makes no sense.
Why does it not make sense? Have you tried other potential solutions?
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#3
(Original post by mqb2766)
Why does it not make sense? Have you tried other potential solutions?
I’m using a maths workbook and the answers are at the back. I have seen people divide 100/3 and get 333.3 and somehow that means it’s 330,332,334 ??????
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2 years ago
#4
(Original post by Aa008)
I’m using a maths workbook and the answers are at the back. I have seen people divide 100/3 and get 333.3 and somehow that means it’s 330,332,334 ??????
Do the 3 numbers satisfy the question or does another set of numbers satisfy the question?
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#5
We can’t be maths geniuses Acsel my friend. ... thanks for the help though
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#6
(Original post by mqb2766)
Do the 3 numbers satisfy the question or does another set of numbers satisfy the question?
The numbers above satisfy the question
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2 years ago
#7
(Original post by Aa008)
We can’t be maths geniuses Acsel my friend. ... thanks for the help though
If you can add the three numbers and check it satisfies the question, I'll happy provide a bit more detail.
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2 years ago
#8
Well for me an algebraic version looks clearer so hopefully this may help. So we'll call the smallest of the 3 possible numbers n. Thats means the next 2 consecutive even numbers will be n+2 and (n+2)+2 or n+4. Since the question asks for the sum of these numbers is less than 1000 we just form an equation out of it. n(the first number)+(n+2)(The next even number)+(n+4)(The next even number after that) < 1000. So n+(n+2)+(n+4) < 1000 since the sum of the numbers is less than 1000. You then solve it. So 3n+6 < 1000. 3n < 994. n < 331.3. The closest even number to 331.3 is 330 so that's our first number since we're looking for the largest possible combination. Then you get the second number, which is n+2, so 332 and then the next number, which is n+4 or 330+4, so 334. Boom, done. Hopefully this clears things up more!
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2 years ago
#9
Oh wait didn't notice it was solved - sorry
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#10
Well for me an algebraic version looks clearer so hopefully this may help. So we'll call the smallest of the 3 possible numbers n. Thats means the next 2 consecutive even numbers will be n+2 and (n+2)+2 or n+4. Since the question asks for the sum of these numbers is less than 1000 we just form an equation out of it. n(the first number)+(n+2)(The next even number)+(n+4)(The next even number after that) < 1000. So n+(n+2)+(n+4) < 1000 since the sum of the numbers is less than 1000. You then solve it. So 3n+6 < 1000. 3n < 994. n < 331.3. The closest even number to 331.3 is 330 so that's our first number since we're looking for the largest possible combination. Then you get the second number, which is n+2, so 332 and then the next number, which is n+4 or 330+4, so 334. Boom, done. Hopefully this clears things up more!
This helped a lot. Thank you!!
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