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

  • Thread starter Thread starter DawnC
  • Start date Start date
  • Tags Tags
    Percent
DawnC
Messages
11
Reaction score
0
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
 
Mathematics news on Phys.org
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
 
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
I'm interested to know whether the equation $$1 = 2 - \frac{1}{2 - \frac{1}{2 - \cdots}}$$ is true or not. It can be shown easily that if the continued fraction converges, it cannot converge to anything else than 1. It seems that if the continued fraction converges, the convergence is very slow. The apparent slowness of the convergence makes it difficult to estimate the presence of true convergence numerically. At the moment I don't know whether this converges or not.
Back
Top