At a factory, two machines pack bottles into boxes for shipping.
Machine A can pack 8 boxes per minute, and Machine B can pack
11 boxes per minute.
1. Before shipment, an inspector found that 7 of the boxes were
defective and could not be shipped. At least 200 boxes were
approved for shipment. Write and solve an inequality to find the
amount of time Machine A spent packing the boxes that were
approved for shipment.
2. The factory receives an order for more than 1,100 boxes. Machine B
has already packed 55 boxes. Write and solve an inequality to find
the amount of time it will take Machine B to pack the additional
boxes that are needed for the order, assuming none of the boxes
are defective.
3. The manager wants the order described in Exercise 2 packed more!
quickly, so she decides to use both Machine A and Machine B to
prepare the shipment. Write and solve an inequality to find the
amount of time it will take both machines to pack the additional
boxes. Explain why the answer is reasonable.
4. Both machines have been packing boxes for some time, and the
difference between the number of boxes that Machine B has
packed and the number of boxes that Machine A has packed is
less than 200. Write and solve an inequality to find the possible
lengths of time to the nearest second that the machines have been
working. Describe the possible solutions.