A technology firm allocated its annual equipment budget among three divisions. The enginee… — ACT

A technology firm allocated its annual equipment budget among three divisions. The engineering division received $\frac{3}{8}$ of the total budget, and the operations division received $30\%$ of the total budget. The remaining $\$52,000$ was allocated to the design division. What was the total equipment budget, in dollars, for the technology firm?

Answer: 160000 dollars

Answer

The total equipment budget for the technology firm was $160,000 dollars.

Converting both allocated parts into decimals gives

\frac{3}{8} = 0.375

for engineering and

30\% = 0.30

for operations. Combined, these two divisions account for

0.375 + 0.30 = 0.675

(or

67.5\%

) of the total budget. The remaining fraction for the design division is

1 - 0.675 = 0.325

(or

32.5\%

). Dividing the design budget of

\$52,000

0.325

yields the total budget of

\$160,000

Step-by-Step Solution

Convert the percentage and fraction to equivalent decimal values.

Engineering receives

\frac{3}{8} = 0.375

, and operations receives

30\% = 0.30

Expressing all portions in decimal form allows for straightforward addition and subtraction.

Sum the portions allocated to the engineering and operations divisions.

0.375 + 0.30 = 0.675

This finds the total proportion of the budget that has already been accounted for.

Determine the remaining decimal portion allocated to the design division.

1 - 0.675 = 0.325

The complete budget represents 1 whole (100%). Subtracting the allocated portions yields the design division's share.

Divide the dollar amount of the design division by its decimal portion to calculate the total budget.

\frac{52,000}{0.325} = 160,000

Since

\text{Design Portion} \times \text{Total Budget} = \text{Design Amount}

, dividing the amount by the decimal portion gives the total budget.

Key Concept

Solving multi-step applied word problems by converting between fractions, decimals, and percentages to determine an unknown total value.

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