Melissa collected 3 kinds of leaves when she was out walking--- elm, maple, and oak. She has 2xs as many maple leaves as elm leaves and 5xs as many oak leaves as elm leaves. Altogether, she has 32 leaves. How many of each kind does she have?
elm leaves === x
maple ==== 2x
oak ===== 5x
solve for x
x + 2x + 5x = 32
E = Elm, M = Maple, O = Oak
M = 2E
O = 5E
O + M + E = 32
Now you just guess & check. Try using the number 8 somewhere; I'm not going to do ALL of it.
o=20 m=4 e=8
To solve this problem, we can set up a system of equations based on the given information.
Let's assume that Melissa has x elm leaves.
According to the problem, Melissa has 2x maple leaves, which is twice as many as elm leaves.
Additionally, Melissa has 5x oak leaves, which is five times as many as elm leaves.
To find the total number of leaves, we can add up the number of elm, maple, and oak leaves:
x + 2x + 5x = 32
Combining like terms, we get:
8x = 32
Dividing both sides by 8, we find:
x = 4
Now that we know the value of x, we can find the number of each kind of leaf that Melissa collected:
Elm leaves: x = 4
Maple leaves: 2x = 2 * 4 = 8
Oak leaves: 5x = 5 * 4 = 20
Therefore, Melissa collected 4 elm leaves, 8 maple leaves, and 20 oak leaves.