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
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?
1 answer
1 answer