Posted by **Shawn** on Saturday, March 16, 2013 at 5:24pm.

Bill brought four times as may apples as harry and three times as may apples as martin. If Bill, and martin purchased less than a total of 190, apples, what is the greatest number of apples that bill could have purchased?

- MATH 112 helpl please -
**Reiny**, Saturday, March 16, 2013 at 7:20pm
apples for Harry -- x

apples for Bill --- 4x

apples for Martin -- y

but Bill's apples = 3 times Martin

4x = 3y

y = 4x/3

Bill + martin < 190

4x + 4x/3 < 190

times 3

12x + 4x < 570

16x < 570

x <35.6

4x < 142.5

greatest number of apples for Bill is 142

but Bill bought 4 times as many as Harry, and we will assume that there were no fractional apples .

Thus Bill's number of apples should be a multiple of 4

and the greatest such multiple which is less than 142

is 140

BUT, that would still give Martin partial apples

how about 136?

then y = (4/3)(136) --- still not a whole number

how about 132 ???

then y = (4/3)(132) = 44 and x = 3y/4 = 33

yeah, whole apples all around

Harry --- 33 apples

**Bill ----- 132 apples**

Martin --- 44 apples

Notice ratio of

Harry : Bill : Martin = 33 : 132 : 44 , where 132 + 44 < 190

= 3: 12: 4

if we went for the ratio of

36 : 144 : 48 , the sum of apples for Bill and Martin > 190

even though the relationship of apples between them would be correct

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