Sally’s employer pays for 32% of her annual health insurance premium of $4,325.00. Sally pays the remaining balance by having it deducted in equal amounts from her 26 paychecks throughout the calendar year. How much will Sally have deducted from each paycheck?

Question

Sally’s employer pays for 32% of her annual health insurance premium of $4,325.00.  Sally pays the remaining balance by having it deducted in equal amounts from her 26 paychecks throughout the calendar year.  How much will Sally have deducted from each paycheck?

tylermckinney16 · Answer

@jdoe0001

mathmale · Answer

1) What is 32% of $4,325?

tylermckinney16 · Answer

$1384

jdoe0001 · Answer

well, Sally's deducted amount, will be
let's see, her employer pays 32% of 4325
so, she has to pay the remaining 68%

we know 4325 is 100%, so, what's the 68% then?
$\bf \begin{array}{ccllll}
quantity&\%
\\hline\
4325&100\
x&68
\end{array}\implies \cfrac{4325}{x}=\cfrac{100}{68}$

mathstudent55 · Answer

Correct.
If the insurance premium is $4325 and the 32% paid by the company is $1384, how much of the $4325 does Sally pay?

mathstudent55 · Answer

total premium = what employer pays + what Sally pays

      4325         =            1384             + what Sally pays

How much does Sally pay?

tylermckinney16 · Answer

$2941

mathmale · Answer

Good.  Now, Tyler, does she pay that $2941 all at once, or what?
How much does she have deducted from each paycheck?

tylermckinney16 · Answer

$26

mathstudent55 · Answer

$" Sally ~pays ~the ~remaining ~balance ~by ~having~ it~ deducted ~in \color{red}{~equal ~amounts}$
$ ~from ~her ~\color{red}{26}~ paychecks~ throughout~ the ~calendar ~year. ~How ~much~ will ~Sally$
$ ~have~ deducted ~from ~each ~paycheck?"$

mathmale · Answer

She has to ;pay $2941 herself.  She can't afford to pay that in one lump sum.  Therefore, she asks her employer to deduct a part of that $2941 from each of her bi-weekly paychecks.  

How many such paychecks are there?

mathmale · Answer

If I agree to pay you $100, but have to do it month-by-month for 5 months, then I end up paying you $100/5, or $20, per month.

How many paychecks does Sally receive in one YEAR?

How much must Sally herself pay, total, for these insurance premiums, per YEAR?

How much will the employer deduct from each paycheck?

mathmale · Answer

Please explain how you arrived at that $26 figure.

tylermckinney16 · Answer

hmm

tylermckinney16 · Answer

$20?

mathstudent55 · Answer

Don't guess.
You already know form above that Sally pays $2941 for her insurance part.
She does it by dividing the amount by 26 equal payments.
If you have to pay $2941 in 26 equal payments, what operation do you do to find out how much each payment is?

mathmale · Answer

Yes, that's correct for my example.  Could you now answer the question you've posted?   As mathstudent55 asks, "If you have to pay $2941 in 26 equal payments, what operation do you do to find out how much each payment is?"

mathmale · Answer

Perform that operation on the following:   $2941 and 26 payments.

mathmale · Answer

Sally has   .... how much? .... deducted from her $2941 share every 2 weeks, or 26 times per year.

tylermckinney16 · Answer

Oh ok i gotcha.

mathmale · Answer

Great.  How much is deducted 26 times per year?

tylermckinney16 · Answer

312?

mathmale · Answer

Show me how you got that, please.  Which math operation did you use?   

Please review what "mathstudent55" wrote to you:  

"Don't guess.
You already know form above that Sally pays $2941 for her insurance part.
She does it by dividing the amount by 26 equal payments.
If you have to pay $2941 in 26 equal payments, what operation do you do to find out how much each payment is?"

tylermckinney16 · Answer

26*12 is what i did

mathmale · Answer

Original post:

"Sally’s employer pays for 32% of her annual health insurance premium of $4,325.00.  Sally pays the remaining balance by having it deducted in equal amounts from her 26 paychecks throughout the calendar year.  How much will Sally have deducted from each paycheck?"

Since Sally's employer pays for 32% of her annual health ins. premium, Sally herself pays the remaining 68%.  Thus, in one year Sally must pay 0.68 times $4,325, or $2941.  Same as before!  She doesn't pay $2941 all at once, but asks her employer to deduct 1/26 of $2941 from each pay check.  What is (1/26) times $2941?

tylermckinney16 · Answer

$113.11

mathmale · Answer

Yes, that's perfect.

In summary:  Sally has to pay (100%-32%) of $4325.  That comes out to 0.68($4325), or $2941.

Sally's employer deducts that sum amount in 26 equal payments of $2941/26 each, or $113.11 each.  End of problem.

mathmale · Answer

This kind of math reasoning becomes easier with practice.

mathmale · Answer

Long explanation!  Hope it helped you.  Thank you for your participation.
When we come to the end of a problem solution, please at least close your post.  A "thanks" would be appreciated.

tylermckinney16 · Answer

Ur welcome :) and sorry it took long to message back im baby sitting

mathmale · Answer

OK.  Good luck.