Algebra 1 : Equations / Solution Sets
Study concepts, example questions & explanations for Algebra 1
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Example Questions
Example Question #5 : Translating Words To Linear Equations
Read, but do not solve, the following problem:
Adult tickets to the zoo sell for $11; child tickets sell for $7. One day, 6,035 tickets were sold, resulting in $50,713 being raised. How many adult and child tickets were sold?
If 
6,035 total tickets were sold, and the total number of tickets is the sum of the adult and child tickets, 
Therefore, we can say 
The amount of money raised from adult tickets is $11 per ticket mutiplied by 
These two equations form our system of equations.
Example Question #6 : Translating Words To Linear Equations
A blue train leaves San Francisco at 8AM going 80 miles per hour. At the same time, a green train leaves Los Angeles, 380 miles away, going 60 miles per hour. Assuming that they are headed towards each other, when will they meet, and about how far away will they be from San Francisco?
Around 3AM the next day, about 1,520 miles away from San Francisco
The two trains will never meet.
Around 10:43AM, about 217.12 miles away from San Francisco
Around 2:45AM, about 200.15 miles away from San Francisco
Around 10:43AM, about 217.12 miles away from San Francisco
This system can be solved a variety of ways, including graphing. To solve algebraically, write an equation for each of the different trains. We will use y to represent the distance from San Francisco, and x to represent the time since 8AM.
The blue train travels 80 miles per hour, so it adds 80 to the distance from San Francisco every hour. Algebraically, this can be written as 
The green train starts 380 miles away from San Francisco and subtracts distance every hour. This equation should be 
To figure out where these trains' paths will intersect, we can set both right sides equal to each other, since the left side of each is 
Since we wrote the equation meaning time for 
To figure out how far from San Francisco they are, figure out how many miles the blue train could have gone in 2.714 hours. In other words, plug 2.714 back into the equation 
Example Question #1 : Translating Words To Linear Equations
We have three dogs: Joule, Newton, and Toby. Joule is three years older than twice Newton's age. Newton is Toby's age younger than eleven years. Toby is one year younger than Joules age. Find the age of each dog.
Joule: 8 years
Newton: 4 years
Toby: 8 year
Joule: 5 years
Newton: Not born yet
Toby: 1 year
Joule: 12 years
Newton: 1 year
Toby: 5 year
none of these
Joule: 9 years
Newton: 3 years
Toby: 8 year
Joule: 9 years
Newton: 3 years
Toby: 8 year
First, translate the problem into three equations. The statement, "Joule is three years older than twice Newton's age" is mathematically translated as
where 
The statement, "Newton is Toby's age younger than eleven years" is translated as
where 
The third statement, "Toby is one year younger than Joule" is
So these are our three equations. To figure out the age of these dogs, first I will plug the third equation into the second equation. We get
Plug this equation into the first equation to get
Solve for 
Divide both sides by 3
So Joules is 9 years old. Plug this value into the third equation to find Toby's age
Toby is 8 years old. Use this value to find Newton's age using the second equation
Now, we have the age of the following dogs:
Joule: 9 years
Newton: 3 years
Toby: 8 years
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