# Proportions - Cooking

by CC

Proportions and Baking Time

If an 2 pound item takes 90 minutes to cook at 350 degrees. how long do you cook it at 300 degrees?

### Comments for Proportions - Cooking

 Mar 17, 2013 Baking Time by: Staff Answer Part I Mathematically, a proportion means that the relationship between variables is a constant. The two variables for this problem are: temperature and time There are several different types of proportions. Direct Proportion An increase in one variable corresponds to an increase in the other variable. Given the variables "x" and "y": y : x = k, a constant value y = kx Inverse Proportion (also called an indirect proportion) An increase in one variable corresponds to a decrease the other variable. Given the variables "x" and "y": y * x = k, a constant value y = k/x Compound Proportion A proportion which involves more than two variables. Given the variables "x", "y", and "z": z = k * y * x k, a constant value k = z / ( x * y) Continued Proportion An ordered set of numbers with the following characteristic: the ratio between every two successive terms is the same. For example, 1:2:4:8:16 k = 2 = 2/1 = 4/2 = 8/4 . . . Exponential proportion y is directly proportional to an exponential function of x Given the variables "x", and "y": y = k * ax both k and a are constant values logarithmic proportion Given the variables "x", and "y": y = k * loga(x) both k and a are constant values To solve this problem, we assume that the lower the temperature, the longer the cooking time. According to Newton's Law of Heating and Cooling, the rate of heating is proportional to the temperature difference between an object being cooked and the temperature of the oven. This is a logarithmic proportion ----------------------------------------

 Mar 17, 2013 Baking Time by: Staff ---------------------------------------- Part II The equation is: t = the cooking time T0 = initial temperature of the food (I will assume to be 75°) Toven = temperature of the oven Tfood = final temperature of the food (I will assume to be 200°) when the oven temperature is 350° the cooking time is 90 minutes The final answer is: Thanks for writing. Staff www.solving-math-problems.com