MHB Calculating Your Average Tax Refund: Tips for Filing Your Taxes in 2021

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The average tax refund for individual filers in January 2021 was $4,120, a decrease of 3.5% from the previous year. To find last year's average refund, the correct equation is x - 0.035x = 4120, which simplifies to 0.965x = 4120. Solving for x gives an approximate value of $4,269.43 for last year's average refund. The discussion clarifies how to combine like terms in the equation, demonstrating the process of factoring and simplifying. Understanding these calculations is essential for accurately determining tax refunds.
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I am wondering if I am starting this question the right way...

As of Jan, the average tax refund sent to individual fliers was \$4,120 down 3.5% from last year. What was the average tax refund last year?

Would the formula to start the problem be: x - 0.035 = \$4120?

Any suggestions would be great
 
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DawnC said:
I am wondering if I am starting this question the right way...

As of Jan, the average tax refund sent to individual fliers was \$4,120 down 3.5% from last year. What was the average tax refund last year?

Would the formula to start the problem be: x - 0.035 = \$4120?

Any suggestions would be great

Welcome to MHB! (Sun)

You are very close...the equation you want is:

$$x-0.035x=4120$$

You see 3.5% of last years refund (which you are calling $x$) would be $0.035x$. Now, can you solve for $x$?
 
MarkFL said:
Welcome to MHB! (Sun)

You are very close...the equation you want is:

$$x-0.035x=4120$$

You see 3.5% of last years refund (which you are calling $x$) would be $0.035x$. Now, can you solve for $x$?

*** I would take x-0.035x = 4120 then I would add x -0.035x(+0.035x) = 4120 +0.035
4120 + 0.035 = 4120.03?
 
DawnC said:
*** I would take x-0.035x = 4120 then I would add x -0.035x(+0.035x) = 4120 +0.035
4120 + 0.035 = 4120.03?

No, you would combine terms on the left to get:

$$0.965x=4120$$

Next, divide both sides by $0.965$ to get (rounded to the nearest penny):

$$x\approx4269.43$$
 
MarkFL said:
No, you would combine terms on the left to get:

$$0.965x=4120$$

Next, divide both sides by $0.965$ to get (rounded to the nearest penny):

$$x\approx4269.43$$

** You mentioned combine like terms. You got 0.965x - how did you get that? Probably very dumb question

- - - Updated - - -

I just practiced on the problem - did you treat (x) as 1?
 
DawnC said:
** You mentioned combine like terms. You got 0.965x - how did you get that? Probably very dumb question

It's just like if you have:

$$a+2a$$

We have one of $a$ and we are adding two $a$'s to it to get three $a$'s:

$$a+2a=3a$$

We can see this also by factoring:

$$a+2a=a(1+2)=a\cdot3=3a$$

So, in your problem, we could write:

$$x-0.035x=x(1-0.035)=x\cdot0.965=0.965x$$

Recall that $x$ is just shorthand for $1\cdot x$. :D
 
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