Exercise 37 Page 376

There are 350 students taking algebra and the ratio of boys to girls is 33:37. We need to find how many more girls than boys are taking the course. To do so we will write and solve a system of equations.

Write a System to Model the Situation

Let b be the number of boys and g be the number of girls taking algebra. As there are 350 students, we can write our first equation as follows. b+ g=350 Let's use the given ratio to write the second equation. The ratio of boys to girls can be written as bg. This fraction we have been told is equal to 33:37= 3337. b/g=33/37 By combining these we find our system of equations. b+ g=350 & (I) b g= 3337 & (II)

Solve the System

When solving a system of equations non-linear terms, such as bg, we must begin by isolating one of the terms. Therefore, we will begin our solution by isolating b in Equation (II). After that we will substitute the resulting expression into Equation (I).

We found that g= 185. To find b, we will substitute 185 for g in Equation (II).

We found that b= 165.

Interpret the Solution

We can interpret this solution, b= 165 and g= 185, as follows. The number of $ boys$ taking algebra is $ 165.$ The number of $ girls$ taking algebra is $ 185.$ The question asks how many more girls than boys are taking the course, so our answer will be 185- 165=20.