melissa collected three kinds of autumn leaves ,oak,elm and maple.she has 2 times as many maple as elm leaves and 5 times as many oak as elm leaves .she has 32 leaves all together. how many of each kind does she have?
4 elm
8 maple
20 oak
Sra
l=32
l=2 (e)
l=5 (e)
l=(2xe)+(5xe)=L
e=4
m=8
o=20
To solve this problem, let's use algebraic equations.
Let's represent the number of elm leaves as 'x'.
According to the problem, Melissa has 2 times as many maple leaves as elm leaves. So, the number of maple leaves is 2x.
Also, Melissa has 5 times as many oak leaves as elm leaves. Hence, the number of oak leaves is 5x.
The total number of leaves Melissa has is given as 32. So, we can write the equation:
x + 2x + 5x = 32
Combining like terms, we get:
8x = 32
Now, let's solve for x by dividing both sides of the equation by 8:
x = 32/8
x = 4
Therefore, Melissa has 4 elm leaves, 2x maple leaves (2 * 4 = 8), and 5x oak leaves (5 * 4 = 20).
In summary, Melissa has:
- 4 elm leaves
- 8 maple leaves
- 20 oak leaves