Padraig recelves total employment compensation of $$ \$ 70,000 $$ and had $$ \$ 2,000 $$ in job expenses. Which of the following could be true about Padraig's gross pay and total employee benefits? a. His total employee benefits are $$ 2.8 \% $$ of his annual gross pay of $$ \$ 72,000 $$. b. His total employee benefits are $$ 2.9 \% $$ of his annual gross pay of $$ \$ 68,000 $$. c. His total employee benefits are $$ 12.5 \% $$ of his annual gross pay of $$ \$ 64,000 $$. d. His total employee benefits are $$ 13.3 \% $$ of his annual gross pay of $$ \$ 60,000 $$. Please select the best answer from the choices provided

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UpStudy AI · Accepted Answer

We start by letting
$$
G = \text{gross pay} \quad \text{and} \quad B = \text{total employee benefits}\,.
$$
An employee’s “total employment compensation” is usually the sum of the gross pay and the benefits. However, if the employee incurs unreimbursed job expenses, his net benefit will be lower. In this problem Padraig’s net benefit (after paying his \$2,000 in job expenses) is given as \$70,000. In other words, his total benefits from employment before paying the expense were larger by \$2,000. This gives us the equation
$$
G + B - 2000 = 70000\,.
$$
Adding back the \$2,000 expense we have
$$
G + B = 72000\,.
$$

Now, let’s check each option to see which pair $$(G,\,B)$$ satisfies the equation $$G + B = 72000$$ (with $$B$$ computed as the stated percentage of $$G$$).

1. Option (a):  
   Gross pay is given as $$G = 72000$$ and the benefits are $$2.8\%$$ of gross pay. Thus,
   $$
   B = 0.028 \times 72000 = 2016\,.
   $$
   Then,
   $$
   G+B = 72000+2016=74016\,.
   $$
   This total is too high since we need it to be $$72000$$.

2. Option (b):  
   Here $$G = 68000$$ and benefits are $$2.9\%$$ of $$68000$$:
   $$
   B = 0.029 \times 68000 = 1972\,.
   $$
   Then,
   $$
   G+B = 68000+1972=69972\,.
   $$
   This sum is too low.

3. Option (c):  
   Now, $$G = 64000$$ and benefits are $$12.5\%$$ of $$64000$$:
   $$
   B = 0.125 \times 64000 = 8000\,.
   $$
   Then,
   $$
   G+B = 64000+8000=72000\,.
   $$
   This exactly satisfies the required total compensation before job expenses. After subtracting the \$2000 expense, Padraig’s net benefit becomes
   $$
   72000-2000=70000\,,
   $$
   which is correct.

4. Option (d):  
   For this choice $$G = 60000$$ and benefits are $$13.3\%$$ of $$60000$$:
   $$
   B = 0.133 \times 60000 = 7980\,.
   $$
   Then,
   $$
   G+B = 60000+7980=67980\,.
   $$
   This sum is too low.

Since only option (c) results in $$G+B=72000$$ and then correct net compensation of $$72000-2000=70000$$, the best answer is:

$$ \boxed{\text{c}} $$.
Padraig's total employee benefits are $$12.5\%$$ of his annual gross pay of \$64,000.

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