Question

The table below shows the relationship between the number of water bottles at a park that are thrown away and the number of water bottles at the park that are recycled for each of five months. Which statement correctly descrīdes the relationship between the number of water bottles that are thrown away and the number of water bottles that are recycled at the park each month? Water Bottles at a Park Water Bottles Water Bottles Thrown Away Recycled 40 12 15 24 80 110 A. The relationship is proportional. For every 3 bottles that are thrown away each month, 10 bottles are recycled. B. The relationship is proportional. For every 10 bottles that are thrown away each month, 3 bottles are recycled. c. The relationship is not proportional. The number of water bottles that are thrown away increases more from month to month than the number of water bottles that are recycled. D. The relationship is not proportional. The difference between the number of bottles that are thrown away and the number of bottles that are recycled is not the same for each month.

Answer 1

EXPLANATION

As we can see in the picture, there is a proportional relationship between the bottles that are thrown away each month and those recycled.

Considering two ordered pairs as for instance, (x_1,y_1)= (40,12) and (x_2,y_2)= (50,15) give us the appropiate rate.

$\text{rate}=\frac{y_2-y_1}{x_1-x_1}$

The rate is as follows:

$rate=\frac{(15-12)}{(50-40)}=\frac{3}{10}\frac{bottles\text{ recycled}}{\text{bottles thrown away}}$

In conclusion, for each 10 bottles thrown away, there are 3 bottles recycled.

The answer is the option B.