Problem Solving

AAPL wrote:Manhattan Prep

A political candidate collected $1,749 from a fund raising dinner. If each supporter contributed at least $50, what is the greatest possible number of contributors at the dinner?

A. 33
B. 34
C. 35
D. 36
E. 37

OA B.

In order to MAXIMIZE the number of contributors, we must MINIMIZE the amount that each supporter contributes.
So, let's say that each supporter contributes exactly $50 (which is the minimum about that each supporter contributes)

$50 divides into $1,749 a total of 34 times (with $49 left over).
So, the maximum number of contributors = 34

Answer: B

Cheers,
Brent

If we want to MAXIMIZE the number of contributors, we must MINIMIZE the contributions of each person.

We want as many people as possible to contribute exactly $50, so think of the greatest multiple of $50 that's less than $1749. 34 people contributing exactly $50 would get us to $1700. Since we have $49 left over, that's not enough for another single contributor, so we can't get to 35. That remaining $49 must have been distributed somehow among the 34 people.

The answer is B.

AAPL wrote:Manhattan Prep

A political candidate collected $1,749 from a fund raising dinner. If each supporter contributed at least $50, what is the greatest possible number of contributors at the dinner?

A. 33
B. 34
C. 35
D. 36
E. 37

To maximize the number of supporters, we should minimize the contribution each supporter made (since the total contribution is fixed, the number of supporters will decrease as the contribution by each supporter increase). Since the minimum possible contribution is 50, let's determine the maximum number of people that contribute 50 dollars.

We can let the number of supporters = x. Thus:

50x = 1749

x = 1749/50 = 34 remainder 49.

Thus, the greatest number of contributors must be 34 people. (Note: The remainder of 49 dollars can be spread to at least 1 of the 34 people. For example, 1 person can contribute 99 dollars while the other 33 people contribute 50 dollars each.)

Answer: B