Chapter 8.2, Problem 54PFA

(a)

To determine

The proportion to represent the number of girls in the school .

Answer to Problem 54PFA

  $\frac{3}{5}$

Explanation of Solution

Given:

At a school, the school population is $\frac{2}{5}$ boys and there are 450 students at the school who are boys.

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 proportion to represent the number of girls in the school, observe the that the proportion of boys is $\frac{2}{5}$ , so subtract it from 1 and simplify further as:

  $\begin{array}{c}1-\frac{2}{5}=\frac{5}{5}-\frac{2}{5}\\ =\frac{5-2}{5}\\ =\frac{3}{5}\end{array}$

Thus, the proportion of girls in school is $\frac{3}{5}$ .

(b)

To determine

The steps to solve the equations.

Explanation of Solution

First from the given equation we find the total number of students in school and then the number of boys in school is given in question. So we can find the number of girls in school.

(c)

To determine

The number of girls in school .

Answer to Problem 54PFA

  $675$

Explanation of Solution

Given:

The population,

  $\frac{2}{5}x=450$

Concept Used:

• To get rid of a number in addition from one side, subtract the same number from both sides of equal sign.
• To get rid of a number in subtraction from one side, add the same number both sides of equal sign.
• To get rid of a number in multiplication from one side, divide the same number from both sides of equal sign.
• To get rid of a number in division from one side, multiply the same number both sides of equal sign.

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 total students in school is x . then since the boys proportion is$\frac{2}{5}$ and the number of boys in school is 450. So, the expression to represent the situation is $\frac{2}{5}x=450$ , now simplify further as shown below:

  $\begin{array}{c}\frac{2}{5}x=450\\ \frac{2}{5}x\cdot 5=450\cdot 5\\ 2x=2250\\ \frac{2x}{2}=\frac{2250}{2}\\ x=1125\text{ Total number of students}\\ \text{ So the number of girls are}\text{.}\\ \text{= }1125-450\\ =675\end{array}$

Thus, the number of girls in school is $675$ .