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Algebra / Linear equations in two variables Difficulty: Easy

A city’s total expense budget for one year was x million dollars. The city budgeted y million dollars for departmental expenses and 201 million dollars for all other expenses. Which of the following represents the relationship between x and y in this context?

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Explanation

Choice B is correct. Of the city’s total expense budget for one year, the city budgeted y million dollars for departmental expenses and 201 million dollars for all other expenses. This means that the expression $y plus 201$ represents the total expense budget, in millions of dollars, for one year. It’s given that the total expense budget for one year is x million dollars. It follows then that the expression $y plus 201$ is equivalent to x, or $y plus 201, equals x$ . Subtracting y from both sides of this equation yields $201 equals, x minus y$ . By the symmetric property of equality, this is the same as $x minus y, equals 201$ .

Choices A and C are incorrect. Because it’s given that the total expense budget for one year, x million dollars, is comprised of the departmental expenses, y million dollars, and all other expenses, 201 million dollars, the expressions $x plus y$ and $2 x minus y$ both must be equivalent to a value greater than 201 million dollars. Therefore, the equations $x plus y, equals 201$ and $2 x minus y, equals 201$ aren’t true. Choice D is incorrect. The value of x must be greater than the value of y. Therefore, $y minus x, equals 201$ can’t represent this relationship.