Chapter 8.4, Problem 21PPS

(a)

To determine

The proportion to model this situation.

Answer to Problem 21PPS

  $\frac{x+3}{x}=\frac{4}{3}$

Explanation of Solution

Given:

The ratio of girls to boys in a class is 4:3 and there are 3 more girls than boys in the class.

Concept Used:

Rules of Addition/ Subtraction:

• Two numbers with similar sign always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similar sign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

Calculation:

Let the number of boys in the class be x . Since there are 3 more girls then the boys in the class, so the number of girls in class would be $x+3$ .

Also given that the ratio of the girls to boys in the class is 4:3, so it gives

  $\frac{x+3}{x}=\frac{4}{3}$

Thus, the proportion to model the given situation is $\frac{x+3}{x}=\frac{4}{3}$ .

(b)

To determine

The number of boys in the class.

Answer to Problem 21PPS

  $9$

Explanation of Solution

Given:

The ratio of girls to boys in a class is 4:3 and there are 3 more girls than boys in the class.

Concept Used:

Rules of Addition/ Subtraction:

• Two numbers with similar sign always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similar sign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

Calculation:

In order to find the number of boys in the class simplify the proportion $\frac{x+3}{x}=\frac{4}{3}$ as shown below

  $\begin{array}{c}\frac{x+3}{x}=\frac{4}{3}\\ 3\left(x+3\right)=4\cdot x\\ 3x+9=4x\\ 3x+9-3x=4x-3x\\ 9=x\\ \Rightarrow x=9\end{array}$

Thus, the number of boys in the class is 9.