How would you solve the following problem?
The ratio of girls to boys in the chess club is a 2 to 1. If there are 10 boys in the chess club, how many girls are there in the club?
Here is one possible way we could reason out the problem. We are told that the ratio of girls to boys is 2 to 1. This ratio must be interpreted as 2 girls to 1 boy because of the order of the words describing the ratio. We draw a diagram of the situation by drawing 2 girls for every 1 boy until we have drawn a total of 10 boys. Let's use B for boy and G for girl. Then our diagram would look like this:
We see from the diagram that when there are 10 boys, there are 20 girls.
Another way to work the problem would be to reason it out by thinking that there are two girls for every one boy (since the ratio of girls to boys is 2 to 1). So, each boy would be paired with two girls. And since we have ten boys each paired with two girls, there must be ten groups of two girls, 10 · 2 = 20. We would conclude that there are 20 girls in the club.
Ratio problems of this type are common where we desire to find an unknown quantity when we know the ratio between it and a known quantity. Some common problem examples would be scaling up or down recipes, mixtures, maps, or architectural drawings.
Though the above problem was not too difficult to reason out, we would like to develop some general methods that would help with more complex problems. Problems of this type are often solved using proportions, which we will introduce later in this lesson.
A recipe calls for three cups of flour for each cup of sugar. How many cups of flour are needed if five cups of sugar are used?
Content ©2010. All Rights Reserved.
Date last modified: July 6, 2010.
Created with SoftChalk LessonBuilder
By Kris Montis and Timothy Peil
