MATH HELPP!!!!!

Question

Including a 19% sales tax, a couch costs $357. Find the original cost of the couch.

A) Write an equation that can be used to solve this question. Use x as the original cost and express any percentage in decimal form.

B) Solve your part [A] equation for x to find the original price of the couch.

Answer 1

$357 = 100%

x = 19%

x = 357 x 19/100

x = 6783/100

x = $67.83 (19% tax)

$357 - $67,83 = $289.17 original price of the couch.

Answer 2

Hey there! This looks like a very good problem to solve with algebra techniques! I will walk you through the easiest way to approach it, as well as others like it.

The first thing to do when approaching problems like these is to identify exactly what it is asking for. In this case, we see that we have to find the original cost of the couch. Next, we take a look at the information we are given: in this case, we know both the sales tax of 19%, along with a $357 cost for the couch. Note that the $357 price is the price of the couch after the 19% sales tax is included. With this knowledge, we can create an equation to find the original price of the couch.

When setting up algebraic equations, a variable is used to represent an unknown value. So, in this case, we can easily represent the original price of the couch with the variable "x", since it is the unknown value we are trying to find. We want our equation to relate x to the information we already know, so that we can use the known information to solve for the unknown information. That's the trick of algebra!

An important thing to note before setting up this equation is that one of the values we are given - the sales tax - is a percentage. In algebra problems like this, it is easiest to convert the percentage to a decimal. This can be easily done, as the percentage means "parts per hundred". So, in the case of 19%, we can write it as the decimal 0.19.

Now comes the fun part - setting up the equation!

Here, we must understand how sales tax works before we can create a correct equation that will give us the original price of the couch. Sales tax is always applied to the original item price. It is written as a percentage to show exactly how much money the tax costs, relative to the original item price. You can find the amount of money a tax costs by multiplying the decimal percentage by the original item price. Here is an example...

A fancy, waterproof paper airplane costs $100. Sales tax is 12%. How much would it cost to buy one of these fancy paper airplanes?

In this case, we can set up an equation that looks like this:

Original cost + Tax cost = Total cost

$100 + (0.12 X $100) = $112

In the paper airplane example above, we have three known values: the original item cost ($100) and the tax rate (12%). From here, we can find the tax rate as (0.12 X $100), which is $12. We find total cost by adding the original cost to the tax cost.

In our couch problem, a couch costs $357 after including a 19% sales tax. This is our total cost. So, we know two things - the total cost ($357) and the tax rate (19%). Our unknown is the original cost. We set this up just like the example above!

Firstly, let's find the tax cost...

Just like in the paper airplane example, tax cost is calculated by multiplying the original cost by the decimal tax rate. Remember, since original cost of the couch is unknown, it is a variable "x". Finding tax cost looks like this:

Tax cost = 0.19 X x = 0.19x

Now we have one term for our equation! Recall that in the paper airplane problem, we added tax cost to original cost to find total cost. We do the same thing here. The only thing different is that we are working with a variable. Here is what the setup process looks like:

Original cost + Tax cost = Total cost

Original cost: we defined as x

Tax cost: we found to be 0.19x

Total cost: we are given as $357

So, our equation becomes:

0.19x + x = $357

Now this is something we can work with! It may look a bit ugly at first, but we can clean it up. Remember that, when solving algebraic equations, we want to have the variable isolated on one side of the equation. In our case, our variable, x, only shows up on the lefthand side of the equation, so we don't need to move it. However, in order to solve this, we will want to make it to where we only have one term with x. Right now, we have two.

Notice that in our equation, we have x + 0.19x. Because these terms have the same variable, x, they can be added. When we add them, we get the following:

1.19x = $357

Remember that the term "x" can also be thought of as "1x". So, when we add 0.19x and x together, we have (1+0.19)x or 1.19x.

Now, we can use algebra to solve this problem for x. Like we noted before, we want to isolate the variable x as much as possible. In our current equation, x is not isolated... it is being multiplied by 1.19. We want x by itself. This means we must get rid of the multiplication on x. How do we do that? With an inverse operation: division!

Dividing 1.19x by 1.19 will cancel out the multiplication, leaving us with 1x, or simply x.

x = $300

Ta-da! And there is our original couch price!

If you are not completely sure about your answer, it is always good to check. So, let's make sure this is correct...

Substitute x = $300 back into our original equation.

(0.19 X $300) + $300 = $357

$57 + $300 = $357

$357 = $357

And that is definitely a true statement! So we know that the answer we found is correct.

The method used to solve this problem can be used to solve many different algebra problems.

Hope I was able to help!

Answer 3

Part A

x = 357 - .19x --> the original cost (x) is (=) 357, what was paid, minus 19% of the original cost (- .19x)

Part B

Now, let's solve for x.

x = 357 - .19x --> add .19x to both sides

1.19x = 357 -->divide by 1.19 to solve for x

x = 300

Therefore the original cost of the couch was $300.

You can verify this by finding 19% of $300 by multiplying 300 by .19, you will get 57, which verifies that the original cost of the couch is indeed $300.