Question

Peter is planting trees in his yard. He wants the ratio of pine trees to oak trees to be 4 to 2. Peter wants to plant a total of 54 trees. How many pine trees should he plant?
A.
38
B.
18
C.
33
D.
36

Answer 1

To determine how many pine trees Peter should plant, we can use the ratio of pine trees to oak trees, which is 4 to 2. This can also be expressed as the ratio 4:2, or simplified to 2:1.

Let \( p \) be the number of pine trees and \( o \) be the number of oak trees. According to the ratio, we can express the number of oak trees in terms of pine trees:

\[
o = \frac{1}{2}p
\]

Peter wants to plant a total of 54 trees, so we have:

\[
p + o = 54
\]

Substituting \( o \) with \( \frac{1}{2}p \):

\[
p + \frac{1}{2}p = 54
\]

Combining like terms:

\[
\frac{3}{2}p = 54
\]

To solve for \( p \), multiply both sides by \( \frac{2}{3} \):

\[
p = 54 \times \frac{2}{3} = 36
\]

Thus, Peter should plant **36 pine trees**. Therefore, the correct answer is:

**D. 36**