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Assume I have four numbers 1 , 3 , 4 , 6

and I have been told to "mark these numbers up" according to the quality scores: 2.1 , 2.4, 2, 0.8

How would I change the proportions of the four numbers according to the qualities scores whist still keeping them summed to 14?

Sorry my minds not working at speed today!!

K
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Chlorophile
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(Original post by mathquestion)
Assume I have four numbers 1 , 3 , 4 , 6

and I have been told to "mark these numbers up" according to the .quality scores: 2.1 , 2.4, 2, 0.8

How would I change the proportions of the four numbers according to the qualities scores whist still keeping them summed to 14?

Sorry my minds not working at speed today!!

K
What do you mean by "Mark up"? Are you multiplying them by the quality score? Or adding them to the quality score? Regardless, once you've got your new set of numbers, you divide it by 14 to find the ratio between the new sum and the old sum of 14, and you then multiply each of the new numbers by that ratio.
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mathquestion
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(Original post by Chlorophile)
What do you mean by "Mark up"? Are you multiplying them by the quality score? Or adding them to the quality score? Regardless, once you've got your new set of numbers, you divide it by 14 to find the ratio between the new sum and the old sum of 14, and you then multiply each of the new numbers by that ratio.

Well neither multiple or add directly. I just want to alter the proportions of the four numbers between eachother using the ratios of the quality scores as a weighting. However I need the four numbers to remain adding up to 14.

these quality scores are corresponding.
1 corresponds to 2.1
3 corresponds to 2.4 etc


ratio of quality scores are: 2.1: 2.4: 2: 0.8
how do I scale up or down the four numbers in line with these proportions?

thanks,
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Chlorophile
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(Original post by mathquestion)
Well neither multiple or add directly. I just want to alter the proportions of the four numbers between eachother using the ratios of the quality scores as a weighting. However I need the four numbers to remain adding up to 14.

these quality scores are corresponding.
1 corresponds to 2.1
3 corresponds to 2.4 etc


ratio of quality scores are: 2.1: 2.4: 2: 0.8
how do I scale up or down the four numbers in line with these proportions?

thanks,
If I understand you correctly, it still follows the same principle. We add those numbers together (to make 7.3) and then find the old set to new set ratio (which is 14/7.3) and then multiply all of the new numbers by this ratio, giving us 4.0, 4.6, 3.8, 1.5 to 1dp. Note that this adds up to 13.9 not 14, because we've rounded these to 1dp. To get a more precise set, you'd need to give more decimal places/significant figures (e.g. 4.03, 4.60, 3.84, 1.53).

Does this answer your question?
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atsruser
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You want 4 numbers a,b,c,d where:

a+b+c+d=14 and a \colon b \colon c \colon d=2.1 \colon 2.4 \colon 2 \colon 0.8

So: a \colon b = 21 \colon 24 \Rightarrow a = \frac{7}{8}b

If you continue in this vain, you can write each variable in terms of, say, d, then calculate the required value of each variable by forming and solving an equation in d.
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