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?
\n","rationale_html":"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 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
is equivalent to x, or
. Subtracting y from both sides of this equation yields
. By the symmetric property of equality, this is the same as
.
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 and
both must be equivalent to a value greater than 201 million dollars. Therefore, the equations
and
aren’t true. Choice D is incorrect. The value of x must be greater than the value of y. Therefore,
can’t represent this relationship.
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