Question

Noah thinks the answers to these two questions will be the same. Do you agree with him? Explain your reasoning. This year, a herd of bison had a 10% increase in population. If there were 550 bison in the herd last year, how many are in the herd this year? This year, another herd of bison had a 10% decrease in population. If there are 550 bison in the herd this year, how many bison were there last year?

Answer 1

Answer: No, She is not right.

Step-by-step explanation:

First question:

Initial number of bison = 550

After increasing 10% than the initial number of bison, the new number of bison after one year= Initial number of bison + 10 % of the initial number of bison

= $110\% \text{ of the initial number of bison}$

= $110\% \text{ of }550$

= $\frac{110\times 550}{100}$

=  $\frac{60500}{100}$

= $605$

Second question:

Let Initial number of bison = x

After decreasing 10% than the initial number of bison, the new number of bison after one year= Initial number of bison - 10 % f the initial number of bison

= $90\% \text{ of the initial number of bison}$

= $90\% \text{ of } x$

= $\frac{90\times x}{100}$

=  $\frac{9x}{10}$

According to the question,

$\frac{9x}{10}=550$

$x=\frac{5500}{9}=611.11\approx 611$

Since, 605 ≠ 611

Therefore, Both questions have different answer.

⇒ Noah is not correct.