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 2000 pounds. Lionel weighs 179 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.
Let x be the weight of each box of books.
The total weight of the boxes of books is 10x.
The total weight of Lionel and the boxes of books is 10x + 179.
We know that 10x + 179 ≤ 2000.
To find the amount each box can weigh, we can solve the inequality:
10x + 179 ≤ 2000
Subtract 179 from both sides:
10x ≤ 1821
Divide both sides by 10:
x ≤ 182.1
So each box can weigh at most 182.1 pounds.
To graph this solution on a number line, we plot the point x = 182.1 and shade in the region to the left of this point.