Question

Rania is playing with her friend Arun, and they are setting dominoes across the room. Each domino is 2 inches long. They have already placed 10 dominoes in a row. The room is 10 feet long and they want to know how many more dominoes they can set up before they reach all the way across the room. Does the inequality 2d + 20 < 120 model this situation? Explain why or why not.​

Answer 1

The inequality 2d + 20 < 120 should actually be 2d + 20 <= 120 to correctly represent the number of remaining dominoes that can be placed across a 10-foot-long room, after 10 dominoes have already been set up.

Step-by-step explanation:

The inequality 2d + 20 < 120 does not correctly model the situation where Rania and Arun are setting up dominoes across a 10-foot-long room. The reasoning is that Rania and Arun have already placed 10 dominoes, each 2 inches long. This contributes 20 inches so far. Since there are 12 inches in a foot, the room is 120 inches long. The inequality should account for the total length left after the 20 inches of dominoes they have already placed.

To model how many more dominoes ('d') they can place, the correct inequality should be 2d + 20 <= 120 because they want to know if they can fit more dominoes within the remaining length of the room. To find out how many more dominoes are needed, subtract the 20 inches already taken by the 10 dominoes from the total length of the room (120 inches) and divide by the length of each domino (2 inches).