One picked 21/2 times as many apples as a second man. A third man picked half as many as the second man. Together they picked a total of 240 apples. How many apples were picked by each man.
Is 21/2 a fraction or division?
A fraction 2 1/2
To solve this problem, we can set up a system of equations. Let's represent the number of apples picked by the second man as x.
The first man picked 21/2 times as many apples as the second man, so he picked (21/2)x apples.
The third man picked half as many apples as the second man, so he picked (1/2)x apples.
Together, they picked a total of 240 apples, so we can write the equation:
x + (21/2)x + (1/2)x = 240
To solve this equation, we can combine like terms:
(2/2)x + (21/2)x + (1/2)x = 240
(24/2)x = 240
Simplifying further:
12x = 240
Now, divide both sides of the equation by 12 to isolate x:
x = 240 / 12
x = 20
So the second man picked 20 apples.
Now, substitute this value back into the equations to find out how many apples the other two men picked:
The first man picked (21/2)x or (21/2) * 20 = 210 apples.
The third man picked (1/2)x or (1/2) * 20 = 10 apples.
Therefore, the second man picked 20 apples, the first man picked 210 apples, and the third man picked 10 apples.