Chapter 8.6, Problem 43PPS

Solution

(a)

The formula for the number of gallons used in a year, that is g, where a car is driven x miles a year and averages m miles per gallon.

  $g=\frac{x}{m}$

Given information:

A car is driven x miles a year and averages m miles per gallon.

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 solve the formula for g , the number of gallons g multiplied by the number of miles per gallon m equals to total number of miles x , so:

  $gm=x$ .

Now solving the formula for g, divide both sides by m to simplify further as shown below:

  $\begin{array}{l}gm=x\\ \frac{gm}{m}=\frac{x}{m}\\ g=\frac{x}{m}\end{array}$

Thus, the formula is $g=\frac{x}{m}$ .

(b)

The formula for the total gas cost c in dollars for driving this car each year.

  $c=pg$

Given:

g is the number of gallons and p is the price per gallon

CALCULATION:

  $\begin{array}{l}g=\text{number of gallons}\\ p=\text{price per gallon}\\ \text{total price c}=p\times g\\ c=pg\end{array}$

Thus, the formula for total cost is

  $c=pg$

(c)

How much money woulde be save on a gas per week by using a car B instead of car A .

Approximately 33 dollars per week

Given:

Car A average 15 miles per gallon on the highway, Car B average 35 miles per gallon on the highway and you average 15000 miles each year.

Cost of gas average is 3 dollar per gallon.

CALCULATION:

In order to find how much money would be save on a gas per week by using car B instead of car A . first car B average 35 miles per gallon on highway, and you average 15000 miles each year, so the number of gallons used to ride 1 year would be $\frac{15000}{35}=428.57\text{gallons}$ .

And then using car A the number of gallons of gas needed in 1 year would be $\frac{15000}{15}=1000$ gallons.

So, the gas saved in 1 year using car B instead of car A is $\text{1000}-\text{428}\text{.57}=\text{571}\text{.43}\text{gallons}$ .

And the money saved in 1 year will be $571.43\times 3=1714.29\text{dollars}$ .

There are 52 weeks in 1 year so the weekly saving should be s $\frac{1714.29}{52}=32.97\approx 33\text{dollars}$ approximately 33 dollars per week.