When deciding between ratios and percents to find the amount of food necessary to restock a restaurant, ratios would be the better choice. Let's say that a restaurant has a popular dish, and a less popular dish. It restocks ingredients for both those dishes, but wants to have twice as much of the popular dish (D1) than the less popular one (D2), or have the ratio 2:1. Now, let's say that D1 requires fish (I1) and salt (I2), and D2 requires bacon (I3) and pepper (I4). If the restaurant is left with 20 units of I1 and 10 units of I2, and knows they want to restock fully to 100 units of I1 and 50 of I2, but lost the information about D2, then the ratio 2:1 can be used to come up with the solution of 50 units of I3 and 25 of I4.
That can be done like this. For I1, 100 is the one that is going to be larger, so we'll put it over the unknown: 100/?. Two is greater than one, so: 2/1. Then a proportion can be written: 100/?=2/1. Using cross-multiplication, which in this case says that the product of the outside numbers must be equal to the product of the inside. So, 100*1=100, but what times two equals 100? 50, of course. So, 100/50=2/1. From that, it can be discovered that 50 units of I3 are needed. Also, the same process can be used to find the answer of 25 units of I4.
The same ratio could also be used in a different situation. Let's say that everything is the same, except for the fact that the restaurant lost the information on D1, instead of D2. Then, the proportion would have to be set up like this: ?/50=2/1. Since 50*2=100, ?*1 must equal 100. Because anything times one is itself, ?, and the number of I1, must be 100. The same can be done to find the