Chapter 8.5, Problem 16IP

To determine

An equation and find the number of miles

Answer to Problem 16IP

The equation is $25+0.45x=40+0.25x$

The total songs are $x=75$ .

Explanation of Solution

Given:

A rental car must be driven for each option to the cost the same for one day

  

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:

In order to find the given equation, let’s assume x be the cost for per milesaccording to the table for A the equation as shown below:

  $A=25+0.45x$

And for B as below:

  $B=40+0.25x$

Both are same for one day, so the equation is $25+0.45x=40+0.25x$

Thus, the equation for both is $25+0.45x=40+0.25x$ .

In order to solve the equation $25+0.45x=40+0.25x$ first subtract both sides by $0.25x$ and then subtract both sides by $25$ and then divide both sides by $0.2$ and then simplify further as below:

  $\begin{array}{c}25+0.45x=40+0.25x\\ 25+0.45x-0.25x=40+0.25x-0.25x\\ 25+0.2x=40\\ 25+0.2x-25=40-25\\ 0.2x=15\\ \frac{0.2x}{0.2}=\frac{15}{0.2}\\ x=75\end{array}$

Thus, the total songs are