Question 193450
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Let <b><i>x</i></b> represent the first part of 94.  Then <b>94 - <i>x</i></b> is the second part.  The fifth part of the first part is:  *[tex \LARGE \frac{x}{5}], and the eighth part of the second part is: *[tex \LARGE \frac{94 - x}{8}].


These two numbers are in the ratio 3:4, so:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{\frac{x}{5}}{\frac{94-x}{8}} = \frac{3}{4}]


Cross-multiply:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{4x}{5} = \frac{3(94-x)}{8} ]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{4x}{5} = \frac{282-3x}{8} ]


Cross-multiply:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 32x = 1410 - 15x]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 47x = 1410]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x = 30]


Check:  The fifth part of 30 is 6, and the eighth part of 64 is 8 and 6 is to 8 as 3 is to 4.


********************************************


Half of A's part is equal to one-third of B's part:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{A}{2} = \frac{B}{3} \ \ \Rightarrow\ \ B = \frac{3A}{2}]


Half of A's part is equal to one-sixth of C's part:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{A}{2} = \frac{C}{3} \ \ \Rightarrow\ \ C = 3A]


Then:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ A + \frac{3A}{2} + 3A = 1980]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2A + 3A + 6A = 3960]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 11A = 3960] 


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ A = 360]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ B = \frac{3(360)}{2} = 540]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ C = 3(360) = 1080]


Check:


Half of 360 is 180, one-third of 540 is 180, and one-sixth of 1080 is 360.  360 + 540 + 1080 = 1980.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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