  # Math Help

<p>Does anyone know how to solve:</p>

<p>Bill Bought 4 times as many apples as Harry and 3 times as many apples as Martin. If Bill, Harry, and Martin purchased less than a total of 190 apples, what is the greatest number of apples that Bill could've purchased?</p>

<p>A) 168, B) 120, C) 119, D) 108, E) 90</p>

<p>I understand how to get the problem to 119, but from there I'm confused about how the problem gets to 108.</p>

<p>harry bought x apples, martin bought y apples, bill bought 4x OR 3y apples. </p>

<p>thus 4x = 3y
y = 4/3 x</p>

<p>so the total amount of apples they bought is 4x + x + 4/3 x = 19/3 x = 190</p>

<p>x = 30</p>

<p>thus bill = 4x = 120</p>

<p>but the question states the total amount is LESS than 190, so the answer has to be LESS than 120, 119 should be the answer. you said the answer in the book is 108, i don't understand that.</p>

<p>EDIT: one potential reason why the answer in the book is 108 is that 108 makes all 3 of them have integer number of apples, bill has 108, harry has 27, and martin has 36.</p>

<p>Nope the answer is 108, this is a tricky one, and I don't know how to figure it out...</p>

<p>Oh I got it!, since B/3= Martin, and B/4= Harry (B=Bill), and they have to be integers the answer has to be divisible by 12 and the closest to that is 12x9= 108. I seriously hope this one doesn't show up on the SAT, because it's extremely tricky...</p>

<p>aye, this one is a little out of the ordinary</p>

<p>You can't purchase a fraction of an apple, so there goes choices C and E. Choice B will give you exactly 190 total apples, but the question is asking you for less than 190. Thus Choice A would definitely go over 190, thereby leaving Choice D as the only possible answer.</p>

<p>For problems like these, it is best to use the answer choices to determine the answer efficiently.</p>

<p>
[quote]
For problems like these, it is best to use the answer choices to determine the answer efficiently.

[/quote]
</p>

<p>I agree; there really isn't a way to find the answer algebraically. Using reason and logic eliminates A (too large), C, and E (C and E will yield fractional numbers of apples). Testing B gives you 190 total apples--too many, given the problem states "less than a total of 190 apples." So, the only choice left is D.</p>

<p>How are you guys testing for answer B?</p>

<p>Nevermind... thanks</p>