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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.

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ashishdwivedilVT

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.

Learn more about equation here:

https://brainly.com/question/10413253

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