In previous math courses, you’ve no doubt run into the infamous “word problems.” Unfortunately, these problems rarely resemble the type of problems we actually encounter in everyday life. In math books, you usually are told exactly which formula or procedure to use, and are given exactly the information you need to answer the question. In real life, problem solving requires identifying an appropriate formula or procedure, and determining what information you will need (and won’t need) to answer the question.
In this chapter, we will review several basic but powerful algebraic ideas: percents, rates, and proportions. We will then focus on the problem solving process, and explore how to use these ideas to solve problems where we don’t have perfect information.
Percents
In the 2004 vice-presidential debates, Edwards’s claimed that US forces have suffered “90% of the coalition casualties” in Iraq. Cheney disputed this, saying that in fact Iraqi security forces and coalition allies “have taken almost 50 percent” of the casualties.[1] Who is correct? How can we make sense of these numbers?
Percent literally means “per 100,” or “parts per hundred.” When we write 40%, this is equivalent to the fraction
40
100
or the decimal 0.40. Notice that 80 out of 200 and 10 out of 25 are also 40%, since
Answers & Comments
Answer:
In previous math courses, you’ve no doubt run into the infamous “word problems.” Unfortunately, these problems rarely resemble the type of problems we actually encounter in everyday life. In math books, you usually are told exactly which formula or procedure to use, and are given exactly the information you need to answer the question. In real life, problem solving requires identifying an appropriate formula or procedure, and determining what information you will need (and won’t need) to answer the question.
In this chapter, we will review several basic but powerful algebraic ideas: percents, rates, and proportions. We will then focus on the problem solving process, and explore how to use these ideas to solve problems where we don’t have perfect information.
Percents
In the 2004 vice-presidential debates, Edwards’s claimed that US forces have suffered “90% of the coalition casualties” in Iraq. Cheney disputed this, saying that in fact Iraqi security forces and coalition allies “have taken almost 50 percent” of the casualties.[1] Who is correct? How can we make sense of these numbers?
Percent literally means “per 100,” or “parts per hundred.” When we write 40%, this is equivalent to the fraction
40
100
or the decimal 0.40. Notice that 80 out of 200 and 10 out of 25 are also 40%, since
80
200
=
10
25
=
40
100