Question

Josiah, the manager of a pet store, bought 72 oz of water conditioner to use in his fish tanks. His small tanks would require 2 oz of conditioner and his large tanks would require 6 oz of conditioner. He made a sketch to show the line representing the different combinations of tanks he could put the water conditioner into. The x-axis represented the number of small tanks and the y-axis represented the number of large tanks. The manager labeled only the intercepts.
Which points did the manager label?



(0, 6) and (2, 0)

(0, 12) and (36, 0)
(6, 0) and (0, 2)
(0, 36) and (12, 0)

Answer 1

Given that the x-axis represented the number of small tanks and the y-axis represented the number of large tanks.

Given that his small tanks would require 2 oz of conditioner and his large tanks would require 6 oz of conditioner and there are a total of 72 oz of water conditioners available.

The line representing the various combinations of tanks he could put the water conditioner into is given by 2x + 6y = 72.

Since, the manager labeled only the intercepts.

The x-intercept is the value of x when y = 0 and is given by

2x + 6(0) = 72

x = 72 / 2 = 36

Thus, the x-intercept is (36, 0)


The y-intercept is the value of y when x = 0 and is given by

2(0) + 6y = 72

y = 72 / 6 = 12

Thus, the x-intercept is (0, 12)

Therefore, the points labeled by the manager are: (0, 12) and (36, 0)