Joe picked leaves, he has 3 kinds. He has 2 times as many elm leaves as maple leaves, and 5 times as many oak leaves as maple. He has 32 leaves. How many of each kind does Joe have?
To solve this problem, let's set up some variables:
Let's say:
M = number of maple leaves
E = number of elm leaves
O = number of oak leaves
From the problem, we know the following:
1) Joe has 2 times as many elm leaves as maple leaves:
E = 2M
2) Joe has 5 times as many oak leaves as maple leaves:
O = 5M
3) Joe has a total of 32 leaves:
M + E + O = 32
Now, let's substitute the values of E and O from equations 1) and 2) into equation 3):
M + (2M) + (5M) = 32
8M = 32
M = 32/8
M = 4
Now that we have the value of M, we can substitute it back into equations 1) and 2) to find the values of E and O:
E = 2M = 2(4) = 8
O = 5M = 5(4) = 20
Therefore, Joe has 4 maple leaves, 8 elm leaves, and 20 oak leaves.