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?
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
To find the greatest number of apples that Bill could have purchased, we need to consider the information given in the question:
1. Bill brought four times as many apples as Harry: Let's say Harry brought x apples. So, Bill brought 4x apples.
2. Bill brought three times as many apples as Martin: Let's say Martin brought y apples. So, Bill brought 3y apples.
Now, we know that the total number of apples purchased by Bill and Martin is less than 190. Therefore, we can write an equation to represent this:
4x + 3y < 190
To find the greatest number of apples Bill could have purchased, we need to maximize the value of 4x while still satisfying the inequality above. Since we want to maximize x, we want to minimize y.
To minimize y, we set it to the smallest value possible. Since y represents the number of apples brought by Martin, it must be a non-negative integer. Therefore, the smallest possible value of y is 0.
Substituting y = 0 into the inequality, we get:
4x + 3(0) < 190
4x < 190
x < 190/4
x < 47.5
Since x must be a non-negative integer as well, the largest possible value of x is 47. Therefore, the greatest number of apples that Bill could have purchased is:
4x = 4 * 47 = 188 apples.