Question

Please I have a 8th grade math question

A tree that is 3 feet tall is growing at a rate of 1 foot per year. A 4 foot tree is growing at a rate of 0.5 foot per year. In how many years will the trees be the same height.


The trees will be the same height in [Blank] years.​

Answer 1

Answer: 2

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Step-by-step explanation:

x = number of years

y = height in feet

The equation for the first tree is

y = x+3

The slope is 1 to represent a rate of 1 ft per year of growth. The y intercept of 3 is the starting height. Refer to y = mx+b form.

For the second tree, the equation is:

y = 0.5x+4

This time we have a slope of 0.5 and a y intercept of 4.

Apply substitution to solve for x

y = x+3

0.5x+4 = x+3

0.5x-x = 3-4

-0.5x = -1

x = -1/(-0.5)

x = 2

The trees will be the same height in 2 years.

What will that height be? Plug x = 2 into either equation to find y. We should get the same y value.

y = x+3

y = 2+3

y = 5

Or we could say

y = 0.5x+4

y = 0.5*2+4

y = 1+4

y = 5

We've shown that both equations lead to y = 5 when x = 2. This means that at the 2 year mark, both trees are 5 feet tall. This helps confirm we have the correct x value.