AnswersAlgebra IIN/A — ExamQuestion 32
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Question 32 • Algebra II

Day and Night Kennel charges 20 dollars per day plus a one-time food fee of 15 dollars to board a pet. Bark Time Hotel charges 30 dollars per day plus a one-time food fee of 5 dollars Which system represents this real-world situation?

Answer
A
Image with description On a coordinate plane, the scale for the x axis range from negative 5 to 5 with an interval of 1 unit, and the scale on y axis range from negative 50 to 50 with an interval of 5 units. Two lines pass through the points (0 comma 5) and (0 comma 30) and intersect each other at (negative 2 point 5 comma negative 20).
B
Image with description Coordinate plane with x-axis and y-axis. Two straight lines intersect at the closed point 1 comma 35. One line has a moderate positive slope and passes through approximately negative 4 comma 10 and 4 comma 50. The second line has a steeper positive slope and passes through approximately negative 4 comma negative 50 and 2 comma 50. Both lines extend indefinitely in both directions as indicated by arrows. The graph shows a single intersection point at 1 comma 35.
C
Image with description Coordinate plane with x-axis and y-axis. Two steep straight lines with positive slopes pass through the closed point 0 comma 0. Both lines extend upward and downward with arrows. One line is slightly steeper than the other, so the lines intersect only at the origin and then diverge as x increases or decreases. The graph shows a single intersection point at 0 comma 0.
D
Image with description Coordinate plane with x-axis and y-axis. Two steep straight lines with positive slopes are shown. One line passes through the closed point 1 comma 35 and extends upward and downward with arrows. The second line is parallel to the first and lies slightly to the left, extending upward and downward with arrows. The lines do not intersect, indicating they have the same slope and different y-intercepts. The closed point 1 comma 35 lies on the right-hand line.

Explanation

Let x be the number of days and y the total cost. Day and Night’s cost is y = 20x + 15, while Bark Time’s cost is y = 30x + 5. Setting the costs equal gives 20x + 15 = 30x + 5, so x = 1 and the shared cost is 35 dollars. The correct choice is B, which shows the two costs intersecting at (1, 35).

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