Divide number into 3 parts with each part being 1.6 times greater than the last

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In summary, a friend posed a question about dividing 90 into three parts where each part is 1.6 times greater than the last. The solution provided was to write an equation as x + 1.6x + 1.6^2x = 90, then factorize and simplify. The conversation also touched on the balance between helping and spoon-feeding, with the suggestion of leading the OP to the answer rather than giving it outright.
  • #1
CF.Gauss
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A friend posed this just for fun but now its really annoying me.

how do you divide 90 into three parts so that each part is 1.6 times greater than the last.
i.e: the second value should be 1.6 times greater than the first and the third value should be 1.6 times greater than the second?

Im confusing myself with this.
Thanks
 
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  • #2
Hi CF.Gauss. Just write it as [itex]x + 1.6 x + 1.6^2 x = 90[/itex] and then factorize out the "x" and simplify.
 
  • #3
uart said:
Hi CF.Gauss. Just write it as [itex]x + 1.6 x + 1.6^2 x = 90[/itex] and then factorize out the "x" and simplify.

Hm ... I thought the goal here was to help people think and understand things, not spoon-feed them answers. Have I got that wrong?
 
  • #4
phinds said:
Hm ... I thought the goal here was to help people think and understand things, not spoon-feed them answers. Have I got that wrong?

Actually I did not give the answer, I left the factorizing and the following arithmetic for the OP to do. This is in effect the first line of what probably be a three line derivation for the OP.

I agree though that it does give away a large part of the overall solution. Sometimes with such a simple question it's hard to know how to give the OP a "start" without giving away too much. :smile:

BTW. To me this looked more like a curiosity question than homework anyway, though of course I don't know that for sure.
 
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  • #5
uart said:
Actually I did not give the answer, I left the factorizing and the following arithmetic for the OP to do. This is in effect the first line of what probably be a three line derivation for the OP.

I agree though that it does give away a large part of the overall solution. Sometimes with such a simple question it's hard to know how to give the OP a "start" without giving away too much. :smile:

BTW. To me this looked more like a curiosity question than homework anyway, though of course I don't know that for sure.

Yeah, I can't argue w/ that. Still, I was going to try to lead him to an equation rather than give it to him.
 

1. How do you divide a number into 3 parts with each part being 1.6 times greater than the last?

To divide a number into 3 parts with each part being 1.6 times greater than the last, you can use the following formula:

First part = x

Second part = 1.6x

Third part = (1.6x) x 1.6 = 2.56x

For example, if the number is 10, the three parts would be: 10, 16, and 25.6

2. Is there a specific term for dividing a number into 3 parts with each part being 1.6 times greater than the last?

Yes, this is known as geometric division or geometric progression.

3. Can this method be applied to any number or are there limitations?

This method can be applied to any number as long as it is a positive integer. If the number is a decimal or a negative integer, the formula would need to be modified accordingly.

4. What is the purpose of dividing a number into 3 parts with each part being 1.6 times greater than the last?

This method is often used in mathematics and science to study geometric patterns and sequences. It can also be used in real-life scenarios such as calculating compound interest or population growth.

5. Are there any alternative methods to dividing a number into 3 parts with each part being 1.6 times greater than the last?

Yes, there are other methods such as using a calculator or manually calculating each part using multiplication. However, using the formula mentioned in the first question is the most efficient and accurate method.

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