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In a family, the father took 1/4 of the cake and he had 3 times as muc

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Bunuel
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In a family, the father took 1/4 of the cake and he had 3 times as muc [#permalink] New post   21 Apr 2022, 08:00
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46% (01:23) correct 54% (01:30) wrong based on 39 sessions
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In a family, the father took 1/4 of the cake and he had 3 times as much as each of the other members had. What is the total number of family members?

(A) 3
(B) 7
(C) 9
(D) 10
(E) 12


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Nidzo
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Re: In a family, the father took 1/4 of the cake and he had 3 times as muc [#permalink] New post   22 Apr 2022, 03:34
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Looking at the cake as a circle, the father eats \(1/4\) of the cake, or \(90^{\circ}\) which leaves \(270^{\circ}\).

We know that \(90^{\circ} = 3x\) and thus \(x = 30^{\circ}\).

\(270÷30 = 9\). There are 9 others, plus the father which means that the family has a total of 10 members.

Answer D
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Re: In a family, the father took 1/4 of the cake and he had 3 times as muc [#permalink] New post   12 Sep 2022, 08:14
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Father ate 1/4 th of the cake.

Cake left = 3/4th
Let x be number of members in the family, minus father.

1/4 = (3/4)*(1/x)*3 =>3/4th of the cake is divided amongst x members.
x=9

Total members = x+1(father) = 10(D)
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Re: In a family, the father took 1/4 of the cake and he had 3 times as muc [#permalink] New post   13 Sep 2022, 00:24
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Bunuel wrote:
In a family, the father took 1/4 of the cake and he had 3 times as much as each of the other members had. What is the total number of family members?

(A) 3
(B) 7
(C) 9
(D) 10
(E) 12

Solution:

We are told that the father had 3 times as much as each of the other members had, this means that each of the other members had equal amount of cake respectively

If we assume that there are n members apart from father, then we can say \(\frac{1}{4}=3\times \frac{1-\frac{1}{4}}{n}\)
\(⇒\frac{1}{4}=3\times \frac{3}{4n}\)
\(⇒n=9\)

Total number of members in the family \(=n+1=10\)

Hence the right answer is Option D
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Re: In a family, the father took 1/4 of the cake and he had 3 times as muc [#permalink]
13 Sep 2022, 00:24
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