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

Answer:

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 $3y+5$

⇒ $\frac{50}{100}(3y+5)$

⇒ $\frac{1}{2}(3y+5)$

The new length  = Original length + Increased length = $(3y+5)+ \frac{1}{2}(3y+5)$

2) Let the original length = 100%

Increase percent of length = 50%

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

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

⇒ $\frac{150}{100}(3y+5)$

⇒ $1.5(3y+5)$

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

$(3y+5)+ \frac{1}{2}(3y+5)$ or $1.5(3y+5)$