Chapter 8.1, Problem 1PSA

a

To determine

To find:The third term of the proportion.

Answer to Problem 1PSA

The third term of the proportion is $\frac{27}{36}$

Explanation of Solution

Given information:The following proportion is given:

  $\frac{3}{4}=\frac{9}{12}$

Formula used:

Multiply by numerator and denominator by 3

Calculation:Every term will have the same ratio, therefore for the third term it will be multiplied by the common ratio i.e. $\frac{3}{3}$$\frac{3}{4}=\frac{9}{12}=\frac{9\times 3}{12\times 3}=\frac{27}{36}$

b

To determine

To find: The means and extremes of the given proportion

Answer to Problem 1PSA

Means of the given proportion: 4 & 9

Extremes of the given proportion: 3 & 12

Explanation of Solution

Given information . $\frac{3}{4}=\frac{9}{12}$

Formula used

  $\begin{array}{l}\frac{\text{a}}{\text{b}}=\frac{\text{c}}{\text{d}}\\ \Rightarrow \text{a:b::c:d}\\ \Rightarrow \text{Means are: b \& c}\\ \text{and extremes are : a \& d}\end{array}$

Calculation

  $\begin{array}{l}\frac{3}{4}=\frac{9}{12}\\ \Rightarrow 3:4::9:12\end{array}$

Means are: 4 & 9

Extremes are: 3 & 12