Chapter 1.7, Problem 8E

Solution

To write: A mathematical expression for the quantity described verbally.

The required mathematical expression is $x-\frac{3x}{100}$ dollars.

Given data:

The verbal expression states: ‘Income after a 3% drop in the current income of x dollars.’

Method/Formula used:

Convert verbal expression into mathematical expression by assume base value x or any other variable.

Calculations:

The given statement has two parts, (1) current income is $ x , (2) the income drops by 3%. The current income ‘ x’ dollar is the base number.

Denote the mathematical expression for income after drop by I that is a function of variable x . Then the expression I has the value,

  $\begin{array}{c}I\left(x\right)=\stackrel{\text{Statement}\text{}\text{(1)}}{\overbracket{currentincome\$x}}\text{then}\stackrel{\text{Statement 2}}{\overbracket{3\%\text{of}x\text{less}}}\\ =x-\frac{3}{100}x\because a\%\text{means}\frac{1}{100}\text{of}a\\ =x-\frac{3x}{100}\end{array}$

Thus, the income x after drop by 3% is $\$\left(x-\frac{3x}{100}\right)$ dollars.

Therefore, the mathematical expression $I\left(x\right)$ for the quantity described verbally is $I\left(x\right)=x-\frac{3x}{100}$ dollars.