Melissa collected 3 kinds of leaves when she was out -elm, maple and oak. She has 2 times as many maple leaves as elm leaves and 5 times as many oak as elm leaves. Altogether she has 32 leaves. How many of each kind does she have?
elm = x
x + 2x + 5x = 32
8x = 32
x = 4
She has 4 elm leaves
x=4 elm leaves
2x=8 maple leaves
5x=20 oak leaves
Let's solve this step-by-step.
Let's assume that Melissa has x elm leaves.
According to the given information, she has 2 times as many maple leaves as elm leaves. So she has 2x maple leaves.
It is also stated that she has 5 times as many oak leaves as elm leaves, which means she has 5x oak leaves.
The total number of leaves is given as 32, so we can write the equation as:
x + 2x + 5x = 32
Combining like terms, we get:
8x = 32
Dividing both sides of the equation by 8, we find:
x = 4
So Melissa has 4 elm leaves, 2(4) = 8 maple leaves, and 5(4) = 20 oak leaves.
To solve this problem, let's represent the number of elm leaves as x.
According to the given information, the number of maple leaves is 2 times the number of elm leaves, so we have 2x maple leaves.
Similarly, the number of oak leaves is 5 times the number of elm leaves, so we have 5x oak leaves.
Altogether, Melissa has 32 leaves, which means the total number of leaves is the sum of the number of elm, maple, and oak leaves.
Therefore, we can write the equation:
x + 2x + 5x = 32
Now, let's simplify the equation by adding like terms:
8x = 32
To solve for x, we can divide both sides of the equation by 8:
x = 32 / 8
x = 4
So, she has 4 elm leaves.
Now, we can find the number of maple leaves by substituting the value of x back into the equation:
2x = 2 * 4
2x = 8
Therefore, she has 8 maple leaves.
Similarly, we can find the number of oak leaves by substituting the value of x back into the equation:
5x = 5 * 4
5x = 20
Hence, she has 20 oak leaves.
In conclusion, Melissa has 4 elm leaves, 8 maple leaves, and 20 oak leaves.