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Difficulty: MediumCaselets and Paragraph-Based Data

A multinational corporation allocated a total annual training budget of 140,000 dollars across its three major divisions: Sales, Information Technology (IT), and Human Resources (HR). According to the financial distribution guidelines, the IT division received exactly 20% more funding than the Sales division. Meanwhile, the HR division was allocated exactly half of the amount given to the IT division. If the HR division dedicates 40% of its allocated training budget specifically to onboarding programs, what is the exact amount (in dollars) spent by the HR division on onboarding?

Answer: 12000 dollars

Answer

12000
By converting the text into an algebraic equation, we establish the Sales budget as xx, IT as 1.2x1.2x, and HR as 0.6x0.6x. The sum 2.8x2.8x equals 140,000 dollars, making x=50,000x = 50,000. The HR division receives 0.6x0.6x, which is 30,000 dollars. Finally, taking 40% of the HR division's 30,000 dollar budget yields 12,000 dollars for onboarding programs.

Step-by-Step Solution

1
Define algebraic variables for each division's allocation.
Sales = xx, IT = 1.2x1.2x, HR = 0.6x0.6x
To translate the relative proportional statements from the paragraph into a solvable mathematical model.
2
Set up an equation representing the total corporate training budget.
x+1.2x+0.6x=140,000x + 1.2x + 0.6x = 140,000
The sum of the three divisional budgets must equal the total allocated amount.
3
Solve the equation for xx to find the Sales division's baseline budget.
2.8x=140,000⇒x=50,0002.8x = 140,000 \Rightarrow x = 50,000
To isolate the base variable from which the other departmental budgets are derived.
4
Calculate the total training budget allocated specifically to the HR division.
HR = 0.6×50,000=30,0000.6 \times 50,000 = 30,000
The question asks about a subset of the HR budget, so the total HR budget must be known first.
5
Calculate 40% of the HR division's budget.
0.40×30,000=12,0000.40 \times 30,000 = 12,000
The paragraph specifies that exactly 40% of the HR training budget goes to onboarding programs.

Key Concept

Extracting quantitative relationships from text to form algebraic equations and calculating sequential percentages.
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Topics

Caselets and Paragraph-Based Data

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