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Zorluk: OrtaFractions, Decimals, and Percentages

A software development company allocated its annual operating budget across three departments: Engineering, Marketing, and Customer Support. Exactly 25\frac{2}{5} of the total budget was allocated to Engineering, and 35%35\% of the total budget was allocated to Marketing. If the remaining budget of $45,000\$45,000 was allocated to Customer Support, what was the company's total annual operating budget?

  1. A
    $60,000\$60,000
  2. B
    $112,500\$112,500
  3. C
    $125,000\$125,000
  4. $180,000\$180,000Cevap
  5. E
    $225,000\$225,000

Cevap

The total annual operating budget of the company was $180,000\$180,000.
To find the total budget, first convert 25\frac{2}{5} to a percentage, which is 40%40\%. Adding Engineering's 40%40\% and Marketing's 35%35\% gives 75%75\% of the total budget. This leaves 100%−75%=25%100\% - 75\% = 25\% for Customer Support. Since Customer Support received $45,000\$45,000, setting 0.25T=45,0000.25 T = 45,000 yields T=45,0000.25=$180,000T = \frac{45,000}{0.25} = \$180,000.

Adım Adım Çözüm

1
Convert the fraction allocated to Engineering into a percentage.
25=40100=40%\frac{2}{5} = \frac{40}{100} = 40\%
Converting all departmental allocations to percentages allows for direct comparison and summation.
2
Calculate the combined percentage allocated to Engineering and Marketing.
40%+35%=75%40\% + 35\% = 75\%
Adding the two known departmental shares determines the total fraction of the budget accounted for.
3
Find the percentage allocated to Customer Support.
100%−75%=25%100\% - 75\% = 25\%
The remaining portion of the 100%100\% total budget belongs to Customer Support.
4
Set up an equation relating Customer Support's dollar allocation to the total budget TT and solve for TT.
0.25T=45,000  ⟹  T=45,0000.25=180,0000.25 T = 45,000 \implies T = \frac{45,000}{0.25} = 180,000
Dividing the dollar amount by its corresponding decimal percentage yields the original total budget.

Anahtar Kavram

Solving word problems involving mixed representations of fractions, decimals, and percentages to find an unknown initial total.
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Fractions, Decimals, and Percentages

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