Question

When Gabriella moved into a new house, she planted two trees in her backyard. At the time of planting, Tree A was 34 inches tall and Tree B was 14 inches tall. Each year thereafter, Tree A grew by 2 inches per year and Tree B grew by 6 inches per year. Let A represent the height of Tree At years after being planted and let B represent the height of Tree B t years after being planted. Write an equation for each situation, in terms of t, and determine the height of both trees at the time when they have an equal height.

Answer 1

The height of both trees is 44 and time is 5 years.

It is required to find the time and height of both trees.

What is equation?

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. Equation, statement of equality between two expressions consisting of variables and/or numbers.

Given:

Tree A:

The tree Original Length-  34 inches

Rate the tree grew every year- 2 inches per year

Equation- 2t+34....(i)

Tree B:

The tree Original Length- 14 inches

Rate the tree grew every year- 6 inches per year

Equation- 6t+14........(ii)

According to given question we have,

By equating equation (i) and (ii)  we get,

2t+34=6t+14

34-14=6t-2t

20=4t

Divide 4 on both sides we get,

t=5 years

By put the value of t in both the equation we have,

Tree A height

2t+34=2*5+34

=44

Tree B height

6t+14=6*5+14

=44

Therefore, the height of both trees is 44 and time is 5 years.

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