Question

A small plant is 2 1 2 212 inches tall. How tall will it be in 3 3 weeks if it grows 3 4 34 inch each week? Which method will NOT give the correct number of inches?

Answer 1

Height of plant:
`4(3)/(4)` inches.

Explanation:

Please consider the attached file for complete question.

We have been given that a small plant is 2 1/2 inches tall. It grows 3/4 inch each week. We are asked to find the height of the tree in 3 weeks.

The total height of tree after 3 weeks would be equal to tree's growth in 3 weeks plus initial height.

`\text{Total height of tree after 3 weeks}=(3)/(4)* 3+2(1)/(2)`

We can rewrite our expression as:

`\text{Total height of tree after 3 weeks}=3* (3)/(4)+2(1)/(2)`

We know that multiplying 3 by 3/4 is same as adding 3/4 3 times.

`\text{Total height of tree after 3 weeks}= (3)/(4)+ (3)/(4)+(3)/(4)+2(1)/(2)`

Therefore, 1st method is incorrect.

Let us find height of the plant

`\text{Total height of tree after 3 weeks}=(9)/(4)+2(1)/(2)`

`\text{Total height of tree after 3 weeks}=(9)/(4)+(5)/(2)`

Make a common denominator:

`\text{Total height of tree after 3 weeks}=(9)/(4)+(10)/(4)`

`\text{Total height of tree after 3 weeks}=(9+10)/(4)`

`\text{Total height of tree after 3 weeks}=(19)/(4)`

`\text{Total height of tree after 3 weeks}=4(3)/(4)`

Therefore, the height of the plant after 3 weeks would be
`4(3)/(4)` inches.