Chapter 1.7, Problem 3GP

(a)

To determine

The number of ounces in any number of pounds.

Answer to Problem 3GP

The equation is $y=16x$ .

Explanation of Solution

Given:

  $1\text{pound}=16\text{ounces}$

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 ounces in any number of pounds. Let we asume that pounds is denoted by y and ounce is denoted by x$1\text{pound}=16\text{ounces}$ , use the unitary method with the given scale and simplify further as shown below,

  $\begin{array}{c}1\text{pound}=16\text{ounces}\\ 1y=16x\\ y=16x\end{array}$

Thus, the equation is $y=16x$ .

(b)

To determine

The number of ounces in $5,8,11,\text{and}13$

Answer to Problem 3GP

The table is below:

x	y
5	80
8	128
11	176
13	208

Explanation of Solution

Given:

  $y=16x$

Calculation:

In order to find the number of ounces in $5,8,11,\text{and}13$ we put the value of x in equation $y=16x$ as shown below:

  $\begin{array}{c}y=16x\\ \text{At}x=5\\ y=16x\\ y=16\cdot 5\\ y=80\\ \text{At}x=8\\ y=16x\\ y=16\cdot 8\\ y=128\\ \text{At}x=11\\ y=16x\\ y=16\cdot 11\\ y=176\\ \text{At}x=13\\ y=16x\\ y=16\cdot 13\\ y=208\end{array}$

Thus, the table for r is below:

x	y
5	80
8	128
11	176
13	208

(c)

To determine

The graph for the realtion.

Answer to Problem 3GP

  

Explanation of Solution

Given:

The pair of points are $\left(5,80\right),\left(8,128\right),\left(11,176\right)and\left(13,208\right)$

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 $\left(5,80\right),\left(8,128\right),\left(11,176\right)and\left(13,208\right)$ and plot in graph as shown below: