A corporate advisory firm executes two types of client projects: Type A and Type B. Each T… — GMAT

A corporate advisory firm executes two types of client projects: Type A and Type B. Each Type A project requires $x$ hours of financial modeling and $y$ hours of executive reporting. Each Type B project requires $x + 3$ hours of financial modeling and $2y - 2$ hours of executive reporting. During the first quarter, the firm completed 6 Type A projects and 4 Type B projects. If the total time spent on financial modeling across all 10 projects was 72 hours and the total time spent on executive reporting was 62 hours, what is the value of $3x + 4y$ ?

Answer: 38

Answer

The value of

3x + 4y

is 38.

Setting up total financial modeling hours gives

6x + 4(x + 3) = 72

, which yields

x = 6

. Setting up total executive reporting hours gives

6y + 4(2y - 2) = 62

, which yields

y = 5

. Substituting these values into

3x + 4y

yields

3(6) + 4(5) = 38

Step-by-Step Solution

Formulate and solve the linear equation for financial modeling hours.

x = 6

6 Type A projects take

6x

hours and 4 Type B projects take

4(x + 3)

hours. Summing them yields

6x + 4x + 12 = 72

, which simplifies to

10x = 60

, giving

x = 6

Formulate and solve the linear equation for executive reporting hours.

y = 5

6 Type A projects take

6y

hours and 4 Type B projects take

4(2y - 2)

hours. Summing them yields

6y + 8y - 8 = 62

, which simplifies to

14y = 70

, giving

y = 5

Substitute

x = 6

and

y = 5

into the targeted expression

3x + 4y

3(6) + 4(5) = 18 + 20 = 38

Key Concept

Linear Equations in One and Two Variables

Question

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