Concept explainers
(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.
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:
Now solving the formula for g, divide both sides by mto simplify further as shown below:
Thus, the formula is
(b)
The formula for the total gas cost c in dollars for driving this car each year.
Given:
g is the number of gallons and p is the price per gallon
CALCULATION:
Thus, the formula for total cost is
(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
And then using car A the number of gallons of gas needed in 1 year would be
So, the gas saved in 1 year using car B instead of car A is
And the money saved in 1 year will be
There are 52 weeks in 1 year so the weekly saving should be s
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Algebra 1, Homework Practice Workbook (MERRILL ALGEBRA 1)
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