Question

A tree grows 1 3/4 per year.How long will it take the tree to grow from a height of 21 1/4 feet to a height of 37 feet?

Answer 1

21.25 + 1.75 = 23
23 +1.75 = 24.75
24.75 + 1.75 = 26.5
26.5 + 1.75 = 28.25
28.25 + 1.75 = 30
30 + 1.75 = 31.75
31.75 + 1.75 = 33.5
33.5 + 1.75 = 35.25
35.25 + 1.75 = 37
Answer is 9 years

Answer 2

A tree grows 1 3/4 per year.

`1(3)/(4) = (7)/(4)`

Rate of growth =slope(m) =
`(7)/(4)` feet per year

Initial height =
`21(1)/(4) = (85)/(4)` feet

Final height = 37 feet

Since there is a constant growth every year , we use linear equation

y= mx+b

Where x is the number of years

b is the initial height and y is the final height

We know the value of m, y and b

Plug in all the values

37 =
`(7)/(4)`* x +
`(85)/(4)`

Now we solve for x, subtract the fraction 85/4 on both sides

37 -
`(85)/(4)` =
`(7)/(4)`* x

`(148-85)/(4)`=
`(7)/(4)`* x

`(63)/(4)`=
`(7)/(4)`* x

Multiply both sides by 4/7

`(63)/(4)`*
`(4)/(7)`=* x

9 = x

So, it will take 9 years to grow to the height of 37 feet.