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If 216 is divided into two parts such that two-third of one part exceeds one-fourth of the other part by 6, then the smaller part is ____.
[tex]If 216 is divided into two parts such that two-third of one part exceeds one-fourth of the other part by 6, then the smaller part is ____.[/tex]
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Answer:
Let, 216 be divided into two parts x and y
[tex]216 = x + y[/tex]
[tex] \frac{2}{3} x = \frac{1}{4} y + 6[/tex]
[tex] y = \frac{8}{3} x - 24[/tex]
[tex]216 = x +( \frac{8}{3} x - 24)[/tex]
[tex]240 = \frac{11}{3} x[/tex]
[tex] \implies x = \frac{720}{11} [/tex]
[tex]y = \frac{240 \times 8}{11} - 24 \\ = \frac{1656}{11} \: \: \: \: \: \: \: \: \: \: [/tex]
So, the smaller part is
[tex] \boxed{x = \frac{720}{11} }[/tex]