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Difficulty: HardFractions, Decimals, and Percentages

A company allocates its annual budget such that 13\frac{1}{3} is spent on Research and Development, 14\frac{1}{4} is spent on Marketing, and the remaining portion is spent on Operations. The Operations budget is then split, with 40%40\% of the Operations budget going to employee salaries and the rest to equipment. If the company spends $150,000\$150,000 on employee salaries in the Operations department, how much money does the company spend on Research and Development?

  1. A
    $48,000\$48,000
  2. B
    $125,000\$125,000
  3. C
    $175,000\$175,000
  4. D
    $200,000\$200,000
  5. $300,000\$300,000Answer

Answer

$300,000\$300,000
The correct answer of $300,000\$300,000 is found by first determining the Operations budget. Since 40%40\% of the Operations budget is spent on salaries and this equals $150,000\$150,000, the Operations budget is $150,0000.40=$375,000\frac{\$150,000}{0.40} = \$375,000. The Research and Development (13\frac{1}{3}) and Marketing (14\frac{1}{4}) budgets combine for 712\frac{7}{12} of the total budget, leaving 512\frac{5}{12} for Operations. We set 512\frac{5}{12} of the total budget equal to $375,000\$375,000, which gives a total budget of $900,000\$900,000. Finally, the Research and Development budget is one-third of the total budget: 13×$900,000=$300,000\frac{1}{3} \times \$900,000 = \$300,000.

Step-by-Step Solution

1
Determine the fraction of the total budget allocated to Operations.
Operations receives 512\frac{5}{12} of the total budget.
The sum of the fractions for Research and Development and Marketing is 13+14=412+312=712\frac{1}{3} + \frac{1}{4} = \frac{4}{12} + \frac{3}{12} = \frac{7}{12}. The remaining fraction for Operations is 1−712=5121 - \frac{7}{12} = \frac{5}{12}.
2
Calculate the budget allocated to the Operations department.
Operations budget is $375,000\$375,000.
Employee salaries account for 40%40\% (or 0.400.40) of the Operations budget and equal $150,000\$150,000. Dividing $150,000\$150,000 by 0.400.40 gives the total Operations budget: $150,0000.40=$375,000\frac{\$150,000}{0.40} = \$375,000.
3
Calculate the total company budget.
Total budget is $900,000\$900,000.
Since the Operations budget of $375,000\$375,000 is 512\frac{5}{12} of the total budget BB, we have 512B=$375,000\frac{5}{12} B = \$375,000. Multiplying both sides by 125\frac{12}{5} yields B=$375,000×125=$900,000B = \$375,000 \times \frac{12}{5} = \$900,000.
4
Calculate the budget spent on Research and Development.
Research and Development budget is $300,000\$300,000.
Research and Development is allocated 13\frac{1}{3} of the total budget: 13×$900,000=$300,000\frac{1}{3} \times \$900,000 = \$300,000.

Key Concept

Solving multi-step word problems using fractions, decimals, and percentage allocations.
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Topics

Fractions, Decimals, and Percentages

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