Welcome to a lesson on writing equations,
we'll be following the guidelines outlined here
for writing equations to solve problems.
Step one, read and understand the problem.
We'll underline the givens, and circle the goal.
Step two, form a strategy to solve the problem.
Step three, choose a variable to represent
the unknown quantity.
Step four, read every word in the problem,
and translate the given information
into an algebraic equation.
Step five, solve the equation.
And finally, step six,
write the answer in a complete sentence.
So in example one, we're given the cost
of leasing a new Ford Mustang I $2,311 for a down payment
and processing fee, plus $276 dollars per month.
For how many months can you lease this car with $10,000?
So, we'll begin by underlining the given information,
which is the down payment is $2,311,
and the monthly payment is $276 per month.
Our goal here is to determine
how many months the car can be leased for $10,000.
Step two, our strategy is going to be
to set up an equation, in order to determine
how many months the car can be leased for $10,000.
And, since the unknown is the number of months,
for step three, we'll choose the variable m
to represent the number of months.
Step four, you want to read every word in the problem,
and translate the given information
into an algebraic equation,
so our equation is going to be a cost equation,
so the cost of leasing a new Ford Mustang
is $2,311, so we'll write down 2,311,
plus the monthly cost of $276 per months,
so we'll have plus 276, times the number of months,
which we now know is m, and we'll set this equal
to 10,000, because we're trying to determine
how many months we can lease the car,
if we have $10,000.
Step five, we want to solve this equation.
This is a basic, two step equation,
so for step one, you want to isolate the variable term,
by adding or subtracting,
so we don't want this 2,311 on the left,
so we'll subtract 2,311 on both sides of the equation.
Now, we'll simplify.
This difference simplifies to zero,
so now we have 276m equals 7,689.
And now, for the last step to isolate the m,
we'll divide both sides by 276,
notice on the left, this simplifies to one m, or just m.
And now, we'll find this quotient.
7,689 divided by 276, notice how the calculator
gives us the decimal approximation.
Let's go ahead and round those to, let's say,
three decimal places, so we'll say m is approximately
27.859.
Remember, m is the number of months
that you can lease the car,
so notice how the value of m is telling us
that you don't have enough money
to lease the car for 28 months.
You only have enough money to lease the car for 27 months,
even though you'll spend a little bit less than $10,000.
So, our last step is to write
the answer in a complete sentence,
which is: You can lease the car for 27 months with $10,000.
Let's look at a second example.
You have just bought a new Sony 55-inch 3D television
for $1,600.
The value of the television set decreases by $250 per year.
How long before the television set is worth half
of its original value.
So again, we'll underline the given information
and circle the goal.
So, the given information is that the television set
costs $1,600 and it decreases by $250 each year.
The goal is to determine how long before the television set
is worth half of its original value.
So, once again, our strategy is going to be
to set up an equation and solve to determine
how long it takes for the television set
to be worth half of its original value.
And, our answer is going to be in years,
because it decreases $250 per year,
so the unknown is the number of years,
so let's go ahead and let our variable be equal to y,
where y equals the number of years.
Now, step four, we'll read the problem again,
and translate the given information
into an algebraic equation.
So, you have just bought a new, Sony 55-inch 3D television
for $1,600.
The value of the television set decreases by $250 per year,
so we'd have minus 250, times the number of years,
which is y.
We want to know when this is going to be equal to
half of the original value,
so we'd have equals one half times 1,600,
and now we want to solve the equation for y.
We'll notice on the right side,
one half times 1,600 would be 800,
so let's go ahead and write this as
1,600 minus 250 y equals 800.
Next step, isolate the variable term
by adding or subtracting,
so we'll subtract 600 on both sides, simplify,
so this difference is zero,
so now he have negative 250 y equals 800 minus 1,600
is -800.
And now, for the last step, to solve for y,
we divide both sides by negative 250.
This simplifies to one y, or just y,
and now we'll find this quotient.
800 divided by -250 is equal to exactly 3.2,
which means it takes 3.2 years
for the television to be worth half of its original value.
In this problem, we can use the exact value for y,
because we're not making monthly payments,
we're just talking about the length of time,
so again, to put the answer in a complete sentence:
The television is worth half of its original value
after 3.2 years.
I hope you found this helpful.