I keep seeing posts on Facebook with the declaration, “Another day and I didn’t use algebra.” I would really like to see this negative view of math, and algebra specifically, changed. Granted, we don’t always have a need to use math beyond basic applications, but yesterday, my wife and I used some fairly complex algebra (by most people’s standards) to determine what time to start our dinner.

We decided to have a nice, family meal before our kids had to go to work. On the menu, a standing rib roast, baked potatoes, fresh green beans, corn, and a salad. So where’s the math? Ideally, having all of the meal completed at one time is desirable and this is where the math comes into play.

The directions for cooking the meat to the desired temperature, rare to medium rare, were as follows: Set the oven temperature at 450 degree and cook for 30 minutes. Turn the oven temperature down to 325 degrees and continue cooking for 13 to 15 minutes per pound. Typical cooking directions, right? Right. We wanted to eat at 3 pm so that the kids didn’t have to rush out the door, so what time did we have to put the roast in the oven? The cooking directions give us a compound linear inequality (linear will keep it simpler to understand). The inequality would look something like this:

30 + 13p < t< 30 + 15p, where p represents the weight of the roast in pounds, and t is the time in minutes required to cook the roast.

Before we go too much further, we have to consider a reasonable domain for the weight of the roast. I have selected a domain of 4 to 15 pounds. In my mind, as warped as it may be, this domain provides reasonable weights of roasts to be prepared (wish mine was on the upper end by the way). A graphical representation would look like this:

The dark region between the two dashed lines represents the range of cooking times for roasts within the domain 4 < p < 15.

The ordered pairs at the lower right of each image represent the minimum and maximum suggested cooking times (in minutes) as suggested by the directions. So, what time did the roast go into the oven? 30 + 148 = 178 minutes (2 hrs 58 mins) and 30 + 166 = 196 minutes (3 hrs 16 mins). To simplify matters, we inserted a digital thermometer to monitor the temperature (130 degrees = medium rare) and settled upon the time of noon to be an appropriate amount of time to allow the roast to cook to be “done” by 3 pm.

Other factors we had to consider were the consistency of temperature of the oven, changing the oven temperature when inserting the potatoes for baking, and the core temperature of the roast prior to roasting it. It is suggested that the meat be close to room temperature prior to cooking. Ours wasn’t; it was 40 degrees, therefore a longer cooking time was necessary.

Some other math we had to do to get dinner on the table was to estimate the time needed to bake potatoes at 325 rather than 350 degrees. Potatoes (medium sized) usually take 60 to 75 minutes to bake at 350 so we estimated an extra 15 minutes to bake at 325. Finally, we had to predict the time needed the time needed to steam the green beans. We planned for a 20 minute time.

Not every person would think about this process in this manner, but before thinking “I’ll never use this outside of the classroom” you may be surprised. Algebra can have delicious results.