One morning each member of Angelas family drank an 8-ounce mixture of

Question

One morning each member of Angela’s family drank an 8-ounce mixture of coffee with milk. The amounts of coffee and milk varied from cup to cup, but were never zero. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. How many people are in the family?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 7

(A) 3
(B) 4
(C) 5
(D) 6
(E) 7

Archit3110 · Answer

milk= m and coffee= c
total family size = p
so we can say
(c/6+m/4) *p = c+m
or say
(2c+3m)*p= 12(c+m)
solving 
p & c have to be +ve integers
so
6-p=p-4
p=5
IMO C

shuvodip04 · Answer

Can you please explain how did you arrive at this equation 6-p=p-4??

Archit3110 · Answer

shuvodip04 
(2c+3m)*p= 12(c+m)
2cp-12c=12m-3mp
2c(p-6)= 3m(4-p)

we are interested to determine the value of P and P cannot be -ve
so 
p-6=4-p
2p=10
p=5

shuvodip04 · Answer

Archit3110

How is 2c = 3m??? Because if 2c=3m then only p-6=4-p . Can you please clarify?

Archit3110 · Answer

shuvodip04 
substitute p=5 you will get 2c=3m in

2c(6-p)=3m(p-4)

basically all c,m,p have to be +ve integers which you would get only at p= 5
...

SirSanguine · Answer

Hi  Bunuel  Please help with an explanation. I am unable to proceed as I dont see a limitation on the portions like each has to be integer. For all I understand there can be infinite number of memebers each one taking a drop of both.

Bunuel · Answer

Let me elaborate the solution above. Let c represent the total amount of coffee, m the total amount of milk, and p the number of people in the family. Since each person consumes a total of 8 ounces of coffee and milk, we have: (c/6 + m/4)p = c + m (2c + 3m)p = 12c + 12m 2c(6 - p) = 3m(p - 4) Given that both c and m are positive, it means that 6 - p and p - 4 must also be positive: 6 - p > 0 gives p < 6 p - 4 > 0 gives p > 4 Thus, 4 < p < 6, so p = 5. Therefore, the answer is C.

bumpbot · Answer

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One morning each member of Angelas family drank an 8-ounce mixture of

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