SOLUTION: If 24 is added to a certain number and the sum is divided by 6, the result is 1 more than 13 of the original number. Find the original number

Question 1023733: If 24 is added to a certain number and the sum is divided by 6, the result is 1 more than 13 of the original number. Find the original number
Found 3 solutions by mathmate, Fombitz, fractalier:
Answer by mathmate(429)   (Show Source): You can put this solution on YOUR website!

Question:
A 4-card poker hand is dealt at random from a standard 52-card deck.
(a) What is the total number of possible hands?
(b) What is the total number of possible hands if the hand contains exactly one heart?

Solution:

One very useful tool is the binomial coefficient, which is in fact the number of possible combinations for r objects taken from n distinct objects:
C(n,r)=n!/(r!(n-r)!)

Say we have 5 fruits, an apple, an orange, a plum, a pear and a banana.
The number of different ways we can choose two fruits out of the five is
C(5,2) [5 choose 2]
=5!/(2!3!)
=120/(2*6)
=10

For a four-card hand from 52 (distinct) cards deck, the idea is the same.

(a) possible hands
C(52,4)
=52!/(4!48!)
=52*51*50*49/(1*2*3*4)
=270725

(b) possible hands with only one heart
We have to have one heart, so we choose 1 heart from the 13 (13 choose 1)
in C(13,1)=13 ways.
We choose the remaining 3 cards from the 39 remaining cards in C(39,3) ways.
C(39,3)=39*38*37/(1*2*3)=9139 ways
So the number of possible hands is the product of 13 and 9139=118807

Answer by Fombitz(32388)   (Show Source): You can put this solution on YOUR website!

Answer by fractalier(6550)   (Show Source): You can put this solution on YOUR website!
Call the number, x. Then we have
(24+x)/6 = 1 + 13x
Multiply by 6 and get
24 + x = 6 + 78x
18 = 77x
x = 18/77
I think you probably wrote the question wrong, but that is the answer for the question as written.
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