p = 0.15t + 3.55, w = 0.45t + 2.05 In the equations above, p and w represent the height, in feet, of a poplar tree and a willow tree, respectively, t months after they were both simultaneously planted. What was the height, in feet, of the poplar tree when both trees were the same height?

We're given the equations that calculates the heights of a poplar and willow tree respectively, both of them based on the number of months that elapses.

We're asked for the height of the poplar tree when it's equal to the willow's. This means that their equations must be equal to each other.

When we solve the set up equation, we find after how many months the trees are at the same height, in which it can be plugged into the poplar tree's equation to find its height (and the willow's).

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Calculating the Final Answer

poplar tree = willow tree

0.15t + 3.55 = 0.45t + 2.05

3.55 = 0.45t + 2.05 - 0.15t

3.55 = 0.30t + 2.05

1.50 = 0.30t

5 = t

After 5 months both trees are at the same height of

p = 0.15(5) + 3.55 = 4.3 feet.