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Converting Ratios to Percentages

A Sum of mone...

Question

A Sum of money 20060 has been divide amongst A, B, and C such that A gets 2/3 of what B gets and B gets 1/4 of what C gets. Finds B's Share

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Solution

$t o t a l space a m o u n t equals 200060 space l e t space a m o u n t space g i v e n space t o space C space equals x space a m o u n t space g i v e n space t o space B equals 1 divided by 4 space t h space o f space C apostrophe s space a m o u n t space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space left parenthesis 1 divided by 4 right parenthesis space asterisk times x space space space space space space space space space space space space space space space space space space space space space equals x divided by 4 space a m o u n t space g i v e n space t o space A equals 2 divided by 3 space r d space o f space B space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals left parenthesis 2 divided by 3 right parenthesis asterisk times left parenthesis x divided by 4 right parenthesis space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 2 x divided by 12 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals x divided by 6 space t o t a l space a m o u n t space equals space a m o u n t space g i v e n space t o space A plus space a m o u n t space g i v e n space t o space B plus space a m o u n t space g i v e n space t o space C space space space space space space space space space space space space space space space space space space space space space space equals x divided by 6 space plus space x divided by 4 space plus space x space space space space space space space space space equals x left square bracket 1 divided by 6 plus space space 1 divided by 4 plus space 1 right square bracket space â�� â�� â�� â�� â�� â�� â�� space space space space space space space space equals x left square bracket fraction numerator 1 asterisk times 2 over denominator 6 asterisk times 2 end fraction plus fraction numerator 1 asterisk times 3 over denominator 4 asterisk times 3 end fraction plus fraction numerator 1 asterisk times 12 over denominator 1 asterisk times 12 end fraction right square bracket space space space space space space space space space l c m left parenthesis 4 comma 6 right parenthesis equals 12 space space space space space space space space equals x left square bracket fraction numerator 2 plus 3 plus 12 over denominator 12 end fraction right square bracket space space space space space space space equals fraction numerator 17 x over denominator 12 end fraction w e space h a v e space t o t a l space a m o u n t equals 20060 equals fraction numerator 17 x over denominator 12 end fraction x equals 20060 asterisk times 12 over 17 space space space space equals 14160 B apostrophe s space s h a r e space equals x over 4 space space space space space space space space space space space equals 14160 over 4 space space space space space space space space space equals 3540$

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