## Problema Solution

A tree next to a fence is 2 feet taller than the fence. One year later the tree grew an additional 0.4 feet. If the ratio of the height of the fence to the height of the tree is now 5:8, how tall is the fence?

## Answer provided by our tutors

Let

'x' represent the height of the fence

'y' represent the height of the tree one year ago

A tree next to a fence is 2 feet taller than the fence means:

y = x + 2

One year later the tree grew an additional 0.4 feet and the ratio of the height of the fence to the height of the tree is now 5:8 means:

x : (y + 0.4) = 5 : 8

x / (y + 0.4) = 5 / 8

Since 0.4 = 4/10 = 2/5 we can write:

x / (y + 2/5) = 5 / 8

We have the following system of equations

y = x + 2

x / (y + 2/5) = 5 / 8

From y = x + 2 we get x = 2 - y

We plug x = 2 - y into x / (y + 2/5) = 5 / 8 and get:

(2 - y) / (y + 2/5) = 5 / 8

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x = 1.08 ft

The fence is approximately 1.08 feet tall.