Finding last year's average tax refund given a 3.5% decrease

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DawnC
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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