Question

Phineas is the lead research scientist in a lab and responsible for ordering supplies and equipment. The lab is out of petri dishes, so Phineas orders 185 of them. The lab uses 12 petri dishes each day.

Explain how you would write a two-variable linear equation for this situation.

Answer 1

Let x = number of days since Phineas ordered the dishes, and let y = number of petri dishes remaining. Each day the lab uses 12 dishes, so the number remaining decreases by 12 per day from the initial 185. The linear equation is

y = 185 − 12x

(Equivalently y = −12x + 185.) Here the slope −12 means a loss of 12 dishes per day and the y-intercept 185 is the starting amount. Domain: x ≥ 0 and y ≥ 0. If you set y = 0 to find when they run out, 185 − 12x = 0 ⇒ x = 185/12 ≈ 15.4, so they will run out during the 16th day.