Question

Suppose the length of the vegetable garden is increased by 50%. The new length can be written as (3y + 5) + 1 2(3y + 5) or 1.5(3y + 5). Explain why both expressions are correct. Then write the new length of the garden in simplified form.

Answer 1

Given:

Length of the garden is represented by :

`3y+5`

The length is increased by 50%.

To find the new length.

Solution:

1) The original length =
`3y+5`

The increase in length will be =
`50%` of
`3y+5`

⇒
`(50)/(100)(3y+5)`

⇒
`(1)/(2)(3y+5)`

The new length = Original length + Increased length =
`(3y+5)+ (1)/(2)(3y+5)`

2) Let the original length = 100%

Increase percent of length = 50%

Total percent of length =
`100\%+50\%=150\%`

New length =
`150%` of
`3y+5`

⇒
`(150)/(100)(3y+5)`

⇒
`1.5(3y+5)`

Thus, the new length of the garden can be represented by both expression :

`(3y+5)+ (1)/(2)(3y+5)` or
`1.5(3y+5)`