We use proportions in so many applications of our everyday lives, often without even realizing it. For example, you may know how many calories are in one serving of ice cream according to the packaging. How many calories will you consume if you eat two scoops instead of one? We use proportions to calculate this answer.

Another example is our delicious chocolate raspberry cake recipe from the start of this unit. From our description, we know our recipe calls for four cups of flour to bake a cake that feeds 10 people. We need to make some adjustments to make a bigger cake. How many cups of flour do we need to bake a cake that feeds 25 people?

In the language of proportions and ratios, we know that four cups of flour work for 10 people. But how many cups of flour work for 25 people? Let's label our unknown amount of flour x, and we can set up our equation to solve our question about proportion:

\frac{4}{10} = \frac{x}{25}

Do you see how solving this proportion leads to x=10? (If not, remember the strategy of "cross multiplying" that converts this equation into the more familiar one 25\times 4 = 10\times x, which is the same as the equation 100 = 10\times x.) Let's go back to our original problem to solve a similar question. Your aunt used two cups of sugar to bake a cake that feeds 10 people. What proportion can we set up to determine how many cups of sugar we need to adjust the cake recipe to feed 25 people?
Back to '6.4 Applications of Proportions'