Chapter 1.7, Problem 8IP

(a)

To determine

The equation that can be used to find the number of quarters q in any number of rolls of quarters r

Answer to Problem 8IP

The equation is $\text{r=40q}$ .

Explanation of Solution

Given:

  $1\text{roll}=40\text{quaters}$

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.

Calculation:

In order to find the number of quarter’s q in any number of rolls of quarter’s r$1\text{roll}=40\text{quaters}$ , use the unitary method with the given scale and simplify further as shown below,

  $\begin{array}{c}1\text{roll}=40\text{quaters}\\ r\text{rolls}=40\times q\text{quaters}\\ \text{r=40q}\end{array}$

Thus, the equation is $\text{r=40q}$ .

(b)

To determine

The number of quarters in 3,4,5,and6 rolls.

Answer to Problem 8IP

The table is below:

r	q
3	0.07
4	0.1
5	0.13
6	0.15

Explanation of Solution

Given:

  $1\text{roll}=40\text{quaters}$

Calculation:

In order to find the number of quarters in 3,4,5, and 6 we put the value of r in equation $\text{r=40q}$ as shown below:

  $\begin{array}{c}r=40q\\ \frac{r}{40}=\frac{40q}{40}\\ \frac{r}{40}=q\Rightarrow q=\frac{r}{40}\\ \text{At}r=3\\ \frac{3}{40}=q\\ \Rightarrow q=0.07\\ \text{At }r=4\\ q=\frac{r}{40}\\ q=\frac{4}{40}\\ q=0.1\\ \text{At}r=5\\ q=\frac{r}{40}\\ q=\frac{5}{40}=0.13\\ \text{At}r=6\\ q=\frac{r}{40}\\ =\frac{6}{40}=0.15\end{array}$

Thus, the table for r is below:

R	Q
3	0.07
4	0.1
5	0.13
6	0.15

(c)

To determine

The graph for the realtion.

Answer to Problem 8IP

  

Explanation of Solution

Given:

The pair of points are $\left(3,0.07\right),\left(4,0.1\right),\left(5,0.13\right),\text{and}\left(6,0.15\right)$

Concept Used:

The x-intercepts are where the graph crosses the x-axis, and the y-intercepts are where the graph crosses the y-axis.

Then, algebraically,

• an x-intercept is a point on the graph where y is zero, and
• a y-intercept is a point on the graph where x is zero.

More specifically,

• an x-intercept is a point in the equation where the y-value is zero, and
• a y-intercept is a point in the equation where the x-value is zero.

Calculation:

In order to plot the points in graph we take all points from the table. The points are $\left(3,0.07\right),\left(4,0.1\right),\left(5,0.13\right),\text{and}\left(6,0.15\right)$ and plot in graph as shown below: