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Algebra / Linear equations in two variables Difficulty: Easy

Last week, an interior designer earned a total of $dollar sign 1,258$ from consulting for $x$ hours and drawing up plans for $y$ hours. The equation $68 x + 85 y = 1,258$ represents this situation. Which of the following is the best interpretation of $68$ in this context?

The interior designer earned $dollar sign 68$ per hour consulting last week.

The interior designer worked $68$ hours drawing up plans last week.

The interior designer earned $dollar sign 68$ per hour drawing up plans last week.

The interior designer worked $68$ hours consulting last week.

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Explanation

Choice A is correct. It's given that $68 x + 85 y = 1,258$ represents the situation where an interior designer earned a total of $dollar sign 1,258$ last week from consulting for $x$ hours and drawing up plans for $y$ hours. Thus, $68 x$ represents the amount earned, in dollars, from consulting for $x$ hours, and $85 y$ represents the amount earned, in dollars, from drawing up plans for $y$ hours. Since $68 x$ represents the amount earned, in dollars, from consulting for $x$ hours, it follows that the interior designer earned $dollar sign 68$ per hour consulting last week.

Choice B is incorrect. The interior designer worked $y$ hours, not $68$ hours, drawing up plans last week.

Choice C is incorrect. The interior designer earned $dollar sign 85$ per hour, not $dollar sign 68$ per hour, drawing up plans last week.

Choice D is incorrect. The interior designer worked $x$ hours, not $68$ hours, consulting last week.