Lionel is loading boxes of books into an elevator to move to the 35th floor of an office building. There are 10 boxes of books, and Lionel wants to make sure he is not exceeding the maximum weight of the elevator, which is 2,000 pounds. Lionel weighs 170 pounds. If each box of books weighs the same amount, how much can each box weigh? Solve this problem and then graph the solution on a number line.(1 point)
Responses
Image with alt text: An illustration shows a number line labeled Weight of Each Box in the Elevator. The number line ranges from 0 to 200 in 50 unit increments. A closed point is plotted at 0. A line extends from that point to the right, connecting with a closed point at 200.
Image with alt text: An illustration shows a number line labeled Weight of Each Box in the Elevator. The number line ranges from 0 to 200 in 20 unit increments. A closed point is plotted at 0. A line extends from that point to the right, connecting with a closed point at 183.
To find out how much each box can weigh, we need to subtract Lionel's weight from the maximum weight of the elevator.
Maximum weight of the elevator = 2,000 pounds
Lionel's weight = 170 pounds
Weight each box can weigh = Maximum weight of the elevator - Lionel's weight
Weight each box can weigh = 2,000 - 170 = 1,830 pounds
Therefore, each box can weigh a maximum of 1,830 pounds.
On the number line, we can mark the weight of each box at 1,830. The number line can range from 0 to 2000 with appropriate increments.
Kris currently has $190 and plans to earn more money each of the 8 weekends this summer. She wants at least $1,625 by the end of the summer. Write and solve an inequality for the amount of money Kris needs to earn each weekend. Which answer choice best interprets the solution in the context of the problem?(1 point)
Let x be the amount of money Kris needs to earn each weekend.
The total amount of money Kris needs to earn over 8 weekends is 8x.
We can write the inequality as:
8x ≥ 1625 - 190
Simplifying the right side of the inequality, we have:
8x ≥ 1435
Dividing both sides of the inequality by 8:
x ≥ 179.375
In the context of the problem, the solution x ≥ 179.375 means that Kris needs to earn at least $179.375 each weekend to reach her goal of having at least $1,625 by the end of the summer.
However, since money cannot be divided into fractional amounts, Kris would need to earn at least $180 each weekend to be able to reach her goal of $1,625.