Question

If total employee benefits are calculated as a percentage of their gross pay, which of the following employees receives the largest percentage of their gross pay in employee benefits?
a.
Employee A: gross pay $32,600 , total job benefits $33,600
b.
Employee B: gross pay $32,900 , total job benefits $34,000
c.
Employee C: gross pay $33,400 , total job benefits $33,900
d.
Employee D: gross pay $33,700 , total job benefits $34,700

Answer 1

Consider all employees.

A.

• gross pay $32,600 - 100%,
• total job benefits $33,600 - x%.

Then

$\dfrac{32,600}{33,600}=\dfrac{100}{x},\\ \\32,600\cdot x=33,600\cdot 100,\\ \\x=\dfrac{33,600\cdot 100}{32,600}=\dfrac{33,600}{326} \approx 103.07.$

Employee A receives 3.07% of gross pay in employee benefits.

B.

• gross pay $32,900 - 100%,
• total job benefits $34,000 - x%.

Then

$\dfrac{32,900}{34,000}=\dfrac{100}{x},\\ \\32,900\cdot x=34,000\cdot 100,\\ \\x=\dfrac{34,000\cdot 100}{32,900}=\dfrac{34,000}{329} \approx 103.34.$

Employee B receives 3.34% of gross pay in employee benefits.

C.

• gross pay $33,400 - 100%,
• total job benefits $33,900 - x%.

Then

$\dfrac{33,400}{33,900}=\dfrac{100}{x},\\ \\33,400\cdot x=33,900\cdot 100,\\ \\x=\dfrac{33,900\cdot 100}{33,400}=\dfrac{33,900}{334} \approx 101.50.$

Employee C receives 1.50% of gross pay in employee benefits.

D.

• gross pay $33,700 - 100%,
• total job benefits $34,700 - x%.

Then

$\dfrac{33,700}{34,700}=\dfrac{100}{x},\\ \\33,700\cdot x=34,700\cdot 100,\\ \\x=\dfrac{34,700\cdot 100}{33,700}=\dfrac{34,700}{337} \approx 102.97.$

Employee D receives 2.97% of gross pay in employee benefits.

Answer: correct choice is B.

Answer 2

The largest percentage of their gross pay in employee benefits is $\boxed{\ 1100}$ in option (c).

Further explanation:

Percentage of gross pay in employee benefit can be calculated as follows,

$\boxed{{\text{Percentage of gross pay in employee benefit}}= {\text{Total job benefit - gross pay}}}.$

Given:

The options ofemployee benefits are as follows,

(a).Employee A: gross pay $32,600, total job benefits $33,600

(b).Employee B: gross pay $32,900, total job benefits $34,000

(c).Employee C: gross pay $33,400, total job benefits $33,900

(d).Employee D: gross pay $33,700, total job benefits $34,700

Explanation:

Percentage of gross pay in employee benefit in option (a) can be calculated as follows,

$\begin{aligned}&{\text{Percentage = Total job benefit - Gross pay}}\\&=33600 - 32600\\&= 1000\\\end{aligned}$

Percentage of gross pay in employee benefit in option (b) can be calculated as follows,

$\begin{aligned}&{\text{Percentage = Total job benefit - Gross pay}}\\&= 34000 - 32900\\&=1100\\\end{aligned}$

Percentage of gross pay in employee benefit in option (c) can be calculated as follows,

$\begin{aligned}&{\text{Percentage = Total job benefit - Gross pay}}\\&=33900 - 33400\\&=500\\\end{aligned}$

Percentage of gross pay in employee benefit in option (d) can be calculated as follows,

$\begin{aligned}&{\text{Percentage = Total job benefit - Gross pay}}\\&= 34700 - 33700\\&= 1000\\\end{aligned}$

Hence, the largest percentage of their gross pay in employee benefits is $\boxed{\ 1100}$ in option (c).

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Answer details:

Grade: College

Subject: Mathematics

Chapter: Investment

Keywords: Gross pay, employee benefits, percentage of their gross pay, largest percentage, job benefits, pensions, employee fund, employer.