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

[DawnC]

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

 

[MarkFL]

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:

\(\displaystyle x-0.035x=4120\)

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

 

[DawnC]

Welcome to MHB! (Sun)

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

\(\displaystyle x-0.035x=4120\)

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?

 

[MarkFL]

*** 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:

\(\displaystyle 0.965x=4120\)

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

\(\displaystyle x\approx4269.43\)

 

[DawnC]

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

\(\displaystyle 0.965x=4120\)

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

\(\displaystyle x\approx4269.43\)

** 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?

 

[MarkFL]

** 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:

\(\displaystyle a+2a\)

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

\(\displaystyle a+2a=3a\)

We can see this also by factoring:

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

So, in your problem, we could write:

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

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