A company allocates a total budget of \4,000 between its marketing and research department… — GRE General Test

A company allocates a total budget of $\$4,000$ between its marketing and research departments. The amount allocated to marketing is $\$400$ more than three times the amount allocated to research. How many dollars are allocated to research?

Answer: 900 dollars

Answer

The amount allocated to research is

900

dollars.

x

represents the research budget, the marketing budget is

3x + 400

. Summing both department allocations gives

x + (3x + 400) = 4,000

. Simplifying this linear equation gives

4x + 400 = 4,000

, leading to

4x = 3,600

and

x = 900

Step-by-Step Solution

Define the unknown variable and express both allocations algebraically.

Let

x

be the research budget. The marketing budget is

3x + 400

The marketing allocation is defined relative to the research allocation.

Formulate a linear equation representing the combined budget.

x + (3x + 400) = 4000

The total budget allocated across both departments is

\$4,000

Solve the linear equation for

x

4x + 400 = 4000 \implies 4x = 3600 \implies x = 900

Combine like terms, isolate the variable term by subtracting

400

, and divide by

4

Key Concept

Setting up and solving a linear equation in one variable from a real-life word problem context.

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