Question last-w

1.1 Linear Functions - Rate of change applications
0:00

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

A.

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

B.

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

C.

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

D.

The interior designer worked 68 hours consulting last week.

Last week, an interior designer earned a total of $ 1,258 from consulting for x hours

Medium-difficulty · SAT Math · Linear Functions — Rate of change applications. Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.

Answer explanation

Choice A is correct. It's given that 68x+85y=1,258 represents the situation where an interior designer earned a total of $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 $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 $85 per hour, not $68 per hour, drawing up plans last week.

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