Mark bought four times as many apples as Harry and three times as many apples as Martin. If Mark, Harry, and Martin purchased less than a total of 190 apples, what's the greatest number of apples that mark could have purchased?
x = Mark's
y = Harry's
z = Martin's
x = 4y so y =1/4 x
x = 3z so z = 1/3 x
x + 1/4 x + 1/3 x < 190
12/12 x + 3/12 x + 4/12 x <190
Solve for x.
168
Let's assume that Harry bought x number of apples.
So, Mark bought 4 times as many apples as Harry, which means Mark bought 4x apples.
And Martin bought 3 times as many apples as Harry, which means Martin bought 3x apples.
Therefore, the total number of apples purchased by Mark, Harry, and Martin is:
x + 4x + 3x = 8x
According to the given information, the total number of apples purchased is less than 190. Therefore:
8x < 190
Dividing both sides of the inequality by 8:
x < 190/8
x < 23.75
Since the number of apples cannot be a fraction, we can round down x to the nearest whole number:
x < 23
Therefore, the greatest number of apples that Mark could have purchased is 4x, which is:
4 * 23 = 92 apples
To find the greatest number of apples that Mark could have purchased, we need to consider the information given.
Let's assume that Harry bought x apples.
It is stated that Mark bought four times as many apples as Harry, so Mark bought 4x apples.
It is also stated that Mark bought three times as many apples as Martin, so Mark bought 3y apples (where y represents the number of apples Martin bought).
Now, we need to consider the given condition that the total number of apples purchased by Mark, Harry, and Martin is less than 190:
x + 4x + 3y < 190
Combining like terms, we have:
5x + 3y < 190
To find the greatest number of apples Mark could have purchased, we need to maximize the value of 4x. We can do this by minimizing the value of x.
Since x represents the number of apples Harry bought, we need to find the smallest possible value for x that satisfies the inequality above.
To minimize x, we set it to its smallest possible value, which is 0. This means that Harry didn't buy any apples.
Plugging in x = 0, the inequality becomes:
5(0) + 3y < 190
3y < 190
Dividing both sides of the inequality by 3, we get:
y < 63.333...
Since y represents the number of apples Martin bought, it must be a whole number. The largest whole number less than 63.333 is 63.
Therefore, the greatest number of apples that Mark could have purchased is:
4x = 4(0) = 0
In conclusion, Mark could have purchased a maximum of 0 apples.