Question

Zack has been planting young trees in his garden. The maple tree that is 42 inches tall is growing 1 inch per month, whereas the oak tree that is 10 inches tall is growing 3 inches per month. In a few months, the two trees will be the same height. How long will that take? What will that height be?

Answer 1

In 16 months, two trees will be of same height

The trees will be of 58 inches tall

Solution:

Let "x" be the number of months

The maple tree that is 42 inches tall is growing 1 inch per month

Thus, equation for maple tree is given as:

Maple tree : 42 + 1 inch (number of months)

Maple tree : 42 + x ------- eqn 1

The oak tree that is 10 inches tall is growing 3 inches per month

Thus, equation for oak tree is given as:

Oak tree : 10 + 3 inch (number of months)

Oak tree : 10 + 3x -------- eqn 1

For two two trees to be equal in height, equate eqn 1 and eqn 2

`42 + x = 10 + 3x\\\\3x - x = 42 - 10\\\\2x = 32\\\\x = 16`

Thus, in 16 months, two trees will be of same height

What will that height be?

Substitute x = 16 in any one eqn

`10+3x = 10 + 3(16) = 10+48 = 58`

Thus the trees will be of 58 inches tall