Hello

amargad0391,

One way to solve problems such as these is by using 'diophantine equations' approach.

This approach is explained very nicely by

mau5 in a similar question. The link to mau5's explanation is -

https://gmatclub.com/forum/joanna-bough ... l#p1201409Applying this approach , we have

Let \(C\) = Number of Chocolate ice creams sold and \(V\) = Number of Vanilla ice creams sold.

\(15C+ 14V = 500\) <---Converting dollars into cents for ease of calculation.

\(C = \frac{{500-14V}}{15}\)

Substituting the answer choices, we can see that the smallest value for \(V\) for which \(C\) is an integer is \(V = 10\) (In this case, \(C = 24\)).

Hence the required answer is C.

I hope you find this useful.

amargad0391 wrote:

Bunuel wrote:

Official Solution:

Albert sells chocolate ice-cream for $0.15 per cup and vanilla ice-cream for $0.14 per cup. If Albert earned $5 during his day's work, what is the least number of vanilla cups he could have sold?

A. 0

B. 5

C. 10

D. 15

E. 20

Let \(C\) and \(V\) denote the number of chocolate ice-creams and vanilla ice-creams sold during the day. The question is what is the least integer \(V\) such that \(0.15C + 0.14V = 5\) or \(15C + 14V = 500\). \(V\) has to end with either 0 or 5 (otherwise \(500 - 14V\) will not end with 0 or 5 and so will not be divisible by 15). \(V\) cannot be 0 because 500 is not divisible by 15. \(V\) cannot be 5 because \(500 - 14*5 = 430\) is not divisible by 15. \(V\) can be 10 as \(500 - 14*10 = 360\) is divisible by 15.

Answer: C

Hi Bunuel,

Is there any other way to solve these kind of problems ? May be by considering linear equations and solving for required answer.

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