Beta Shoes has two types of employees: factory wor

Question

Beta Shoes has two types of employees: for every 5 factory employees there are 4 office employees. Employees may enroll in two plans, a dental plan and a pension plan. The percentages of employees enrolled in the dental and pension plans are shown below.

Workers ———- Dental Plan ——— Pension Plan
Factory ————— 20%——————- 80%
Office ——-———- 45%——————- 90%

If there are 72 more employees enrolled in the pension plan than in the dental plan, how many more factory employees than office employees are there?

A. 12
B. 14
C. 15
D. 18
E. 20

Dereno · Answer

Factory employees : Office employees = 5 : 4. Let’s take it as 50x : 40x

Factory workers  :

Dental plan = 20%*(50x) = 10x

Pension plan = 80%(50x) = 40x

Office Workers :

Dental plan = 45%*(40x) = 18x

Pension plan = 90% (40x) = 36x

Total Dental plan = 28x

Total pension plan = 76x

Difference = 76x -28x = 72

48x = 72

x = 1.5

How much is Factory worker more than Office workers = 50x - 40x = 10x = 10*1.5 =  15

Option C

cumquequos · Answer

to solve it first *10 to make it more undersandable:

20% =10
80% = 40
45% = 18
90% = 36

add it to get 76 - 28 = 48

720 / 48 ?

for a quick way to guess 72 - 48 = 24 that happens to be the half of 48 so 48*15 =72

answer 15 = C

Edskore · Answer

Key concept being tested: Ratio-based Word Problems with Percentages (Problem Solving)

The smart move on this question is to assign a concrete multiple immediately. Since the factory-to-office ratio is 5:4, let F = 5k and O = 4k.

1. Set up the dental plan totals:
 Factory dental: 20% of 5k = k
 Office dental: 45% of 4k = 1.8k
 Total dental = 2.8k

2. Set up the pension plan totals:
 Factory pension: 80% of 5k = 4k
 Office pension: 90% of 4k = 3.6k
 Total pension = 7.6k

3. Use the given condition — pension exceeds dental by 72:
 7.6k - 2.8k = 4.8k = 72
 So k = 15

4. Factory minus office employees = 5k - 4k = k = 15

Answer: C (15)

Common trap: Students often set up the equation correctly but then answer "how many factory employees are there?" (which would be 75) instead of the actual question — how many MORE factory than office. The answer they want is just k, which equals 15. Also, some students forget to apply the 5:4 ratio at all and treat F and O as independent variables, leading to an underdetermined system.

The elegant insight here: since F - O = 5k - 4k = k, you don't even need to separately compute F and O. As soon as you find k, you have the answer.

Takeaway: In ratio-word problems, assign variables as multiples of the ratio immediately (5k, 4k rather than two separate unknowns) — it often reduces the algebra significantly.

Beta Shoes has two types of employees: factory wor

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