At a research institute, an annual equipment budget is distributed among three departments… — GRE General Test

At a research institute, an annual equipment budget is distributed among three departments. First, $\frac{2}{5}$ of the total budget is allocated to the Biology department. Next, $\frac{3}{8}$ of the remaining budget is allocated to the Chemistry department. The Physics department receives the remaining balance of $\$45,000$ . What was the institute's total annual equipment budget?

A
$100,000
B
$112,500
$120,000Answer
D
$180,000
E
$200,000

Answer

$120,000

Subtracting the Biology department's share of

\frac{2}{5}

leaves

\frac{3}{5}

of the total budget. The Chemistry department receives

\frac{3}{8}

of this remainder, leaving

\frac{5}{8}

of the remainder for the Physics department. Multiplying these fractions yields

\frac{5}{8} \times \frac{3}{5} = \frac{3}{8}

of the total budget for Physics. Equating

\frac{3}{8}

of the total budget to

\$45,000

gives a total budget of

\$120,000

Step-by-Step Solution

Determine the fraction of the budget remaining after the Biology allocation.

The remaining fraction is

1 - \frac{2}{5} = \frac{3}{5}

of the total budget.

The Biology department receives

\frac{2}{5}

of the overall budget.

Calculate the fraction of the total budget allocated to Physics.

The Physics department receives

1 - \frac{3}{8} = \frac{5}{8}

of the remaining budget, which equals

\frac{5}{8} \times \frac{3}{5} = \frac{3}{8}

of the total budget.

The Chemistry department receives

\frac{3}{8}

of the remaining budget, leaving

\frac{5}{8}

of that remainder for Physics.

Solve for the total budget

B

\frac{3}{8}B = 45,000 \implies B = 45,000 \times \frac{8}{3} = 120,000.

The Physics allocation of

\$45,000

represents

\frac{3}{8}

of the total budget

B

Key Concept

Sequential Fraction of Remainder Calculations

Estimated Time:1m 30s

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