A company used two machines A and B with different printing rates to print stickers. The graphs below show the total number of stickers printed by each machine from 1 p.m.

  1. (a)

    Tick (True / False / Not Possible to Tell) for each statement.

    StatementTrueFalseNot Possible to Tell
    Machine B printed 40 more stickers than machine A in the first hour.
    Machine A took 30 minutes less than machine B to print 400 stickers.
    Machines A and B printed a total of 640 stickers in 12\frac{1}{2} hours.
  2. (b)

    Both machines did not change their rates of printing throughout. When machine B had printed 800 stickers, how many stickers had machine A printed?

    Ans:

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Worked solution

17(a)

1. Evaluate Statement 1: Machine B printed 40 more stickers than machine A in the first hour.

From the graphs, at 2 p.m. (after 1 hour):
Machine A printed 160160 stickers.
Machine B printed 200200 stickers.
Difference =200−160=40= 200 - 160 = 40.
Statement 1 is True.

2. Evaluate Statement 2: Machine A took 30 minutes less than machine B to print 400 stickers.

From the graphs, to print 400 stickers:
Machine B took until 3 p.m., which is 22 hours.
Machine A prints at 160160 per hour. Time taken =400160=2.5= \frac{400}{160} = 2.5 hours (22 hours 3030 minutes).
Machine A took 3030 minutes more than Machine B, not less.
Statement 2 is False.

3. Evaluate Statement 3: Machines A and B printed a total of 640 stickers in $\frac{1}{2}$ hours.

In 12\frac{1}{2} hour (30 minutes):
Machine A prints 1602=80\frac{160}{2} = 80 stickers.
Machine B prints 2002=100\frac{200}{2} = 100 stickers.
Total =80+100=180= 80 + 100 = 180 stickers.
180≠640180 \neq 640.
Statement 3 is False.

Answer

Statement 1: True
Statement 2: False
Statement 3: False

17(b)

1. Determine the time taken for machine B to print 800 stickers

From Graph 2, machine B prints 800800 stickers at 5 p.m.5\text{ p.m.}
Time taken from 1 p.m.1\text{ p.m.} to 5 p.m.5\text{ p.m.} is 44 hours.

2. Calculate the number of stickers machine A prints in the same time

From Graph 1, machine A prints 160160 stickers per hour.
In 44 hours, machine A prints 160×4=640160 \times 4 = 640 stickers.

Answer

640640

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