A startup hired two freelance software developers, Developer A and Developer B, for a comb… — GRE General Test

A startup hired two freelance software developers, Developer A and Developer B, for a combined total of $45$ hours on a single project. Developer A charges $\$65$ per hour, and Developer B charges $\$80$ per hour. If the total amount paid to both developers was $\$3{}225$ , how many hours did Developer A work on the project?

Answer: 25 hours

Answer

Developer A worked on the project for 25 hours.

Let

x

be the hours Developer A worked and

y

be the hours Developer B worked. From

x + y = 45

, we get

y = 45 - x

. Substituting into

65x + 80y = 3225

yields

65x + 80(45 - x) = 3225

. Expanding gives

65x + 3600 - 80x = 3225

, which simplifies to

-15x = -375

, so

x = 25

Step-by-Step Solution

Set up a system of linear equations representing the total hours and total cost.

x + y = 45

and

65x + 80y = 3225

, where

x

is Developer A's hours and

y

is Developer B's hours.

Translating the verbal conditions into mathematical equations.

Express

y

in terms of

x

from the hours equation.

y = 45 - x

Prepares the linear system for substitution.

Substitute

y = 45 - x

into the total cost equation and solve for

x

65x + 80(45 - x) = 3225 \implies -15x = -375 \implies x = 25

Solves for the requested variable

x

directly.

Key Concept

Solving word problems using 2x2 systems of linear equations via substitution or elimination.

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