A certain contest awarded $125 for each first prize, $40 for each seco

Question

A certain contest awarded $125 for each first prize, $40 for each second prize and $15 for each third prize. What is the fewest number of prizes that could be awarded for a total of $1,735 ?

(A)12
(B)14
(C)15
(D)17
(E)18

Ash381 · Accepted Answer

125x+40y+15z=1735.

Our task here is to maximize x. 
125*13=1625

1735-1625 = 110 .

now we maximize y, 40*2=80 , 40*3=120, so we go with 40*2. 
110-80=30.

therefore z =2.

Finally, we have z=2,y=2 and x=13. x+y+z = fewest number of prizes = 17

Bunuel · Answer

A certain contest awarded $125 for each first prize, $40 for each second prize, and $15 for each third prize. What is the fewest number of prizes that could be awarded for a total of $1,735 ? (A) 12 (B) 14 (C) 15 (D) 17 (E) 18 Assume x $125 prizes, y $40 prizes, and z $15 prizes were given. Then, we'd have: 125x + 40y + 15z = 1,735 Reduce by 5: 25x + 8y + 3z = 347 Our goal is to minimize x + y + z. To achieve this, we need to maximize the number of the largest prize, x. The value of x cannot be 14 or higher, so we try x = 13. In this case, we have: 25*13 + 8y + 3z = 347 8y + 3z = 22 Now, let's maximize the number of the next largest prize, y. The maximum value of y is 2, making z = 2. Therefore, x + y + z = 13 + 2 + 2 = 17. Answer: D. Similar question to practice: https://gmatclub.com/forum/the-first-pr ... 21161.html

oiploiloi · Answer

D

Because you want the fewest number of prizes, use up as much of the largest prize (125 dollars each) as possible
= 13 first-place prizes for 1625 dollars, leaving 110 dollars
Use up the next largest prize (40 dollars)
= 2 second-place prizes for 80 dollars, leaving 30 dollars to use up
Use up the final prize (15 dollars)
= 2 third-place prizes for 30 dollars, leaving nothing!

Add up: 13 + 2 + 2 = 17 prizes

ifra94 · Answer

Is there a faster way to do this? I simplified the equation to simpler numbers :

25x+8y+ 3z = 347

Then I wrote down all possible combinations of y and z = selected the one that would give me a multiple of 25.

DanTheGMATMan · Answer

To minimize the number of prizes given, maximize the number of top prizes given, and then work out the remainder from there:

https://www.youtube.com/watch?v=Fg6rHbfXEFE

ShubhamSS28 · Answer

A simpler approach is to understand the problem first

total value of fewest number of prizes = $1735

1st prize = 1735/125 = 13.88 --> Let us consider 13 number of prizes worth $125 so we are now left with (1735 - 13 x 125) = 110

2nd prize ($40) and 3rd prize ($15) to make 110 
following the same approach as above
(2 x 40) + (2 x 15) = 110

Fewest number of prizes = 13 + 2 + 2 = 17

A certain contest awarded $125 for each first prize, $40 for each seco

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A certain contest awarded $125 for each first prize, $40 for each seco

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