Question

When Gavin moved into a new house, he planted two trees in his backyard. At the time of planting, Tree A was 38 inches tall and Tree B was 22 inches tall. Each year thereafter, Tree A grew by 4 inches per year and Tree B grew by 8 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, commat, and determine the number of years after the trees were planted when both trees have an equal height.

Answer 1

Both trees will have an equal height after 4 years. The equation for the height of Tree A is AA = 38 + 4t and for Tree B is BB = 22 + 8t.

Step-by-step explanation:

The equation for the height of Tree A (AA) after tt years can be represented as AA = 38 + 4t, where 38 is the initial height and 4 is the growth rate per year.

The equation for the height of Tree B (BB) after tt years can be represented as BB = 22 + 8t, where 22 is the initial height and 8 is the growth rate per year.

To determine the number of years when both trees have an equal height, we need to set the equations equal to each other and solve for t:

38 + 4t = 22 + 8t

Subtract 4t from both sides:

38 = 22 + 4t

Subtract 22 from both sides:

16 = 4t

Divide both sides by 4:

t = 4

Therefore, both trees will have an equal height after 4 years.