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When Joseph moved into a new house, he planted two trees in his backyard. At the time of planting, Tree A was 16 inches tall and Tree B was 37 inches tall. Each year thereafter, Tree A grew by 6 inches per year and Tree B grew by 3 inches per year. Let AA represent the height of Tree A tt years after being planted and let BB represent the height of Tree B tt years after being planted. Write an equation for each situation, in terms of t,t, and determine the interval of time, t,t, when Tree A is taller than Tree B.

Answer :

The tree A is 3t taller than tree B.

Equation to represent tree A = 16 + 6t

Equation to represent Tree B= 37+ 7t

What is linear equation?

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.

Given that : Tree A was 16 inches tall and Tree B was 37 inches tall.

Tree after 't' year

A= 16 + 6t

B = 37 + 7t

so,

A-B= 16 + 6t -(37+3t)

    = 16 + 6t - 37 -3t

    = 3t- 21

As tree A grew 2 times the tree B

then t'= 2t

A'- B'= 3t' -21

        = 3(2t)-21

        =6t -21

Thus, (A'- B')(A-B) = 6t-21- (3t-21)

                   = 6t-3t

                   = 3t

Hence the tree A is 3t taller than tree B

Equation to represent Tree A = 16 + 6t

                                     Tree B= 37+ 7t

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