The given scatterplot shows the
print speed and cost per newspaper for 19 newspaper companies, and the line of best
fit for the data. It takes the company with the
slowest printing speed in this group 𝑘 minutes longer to print 650 newspapers than
the company with the fastest printing speed. Which of the following is closest
to 𝑘? A) 54, B) 540, C) five, or D)
For us to calculate 𝑘, the amount
of time longer it takes the slowest company to print 650 newspapers than the fastest
company, we first need to find the print speeds of the slowest and fastest
companies. Let’s start with the fastest. The 𝑥-axis tells us the print
speed. And the higher the number, the more
newspapers that are printed in tens per minute. The more newspapers you can print
per minute, the faster you are. And so, the fastest company will be
the company that is furthest to the right on the 𝑥-axis.
We need to look at the
𝑥-coordinate of the fastest speed. The company with the fastest speed
is located just below 14 tens of newspapers per minute. The fastest company prints 13.9
tens of newspapers per minute. The slowest company will be the
company that prints the least amount per minute. That’s going to be the company that
is furthest to the left on the 𝑥-axis.
If we draw a line to indicate where
along the 𝑥-axis this point is, it’s slightly above halfway between zero and
two. We could maybe call it 1.1. But we have to remember the 𝑥-axis
is measured in tens, so we say 1.1 tens per minute. At this point, we could simplify
the 13.1 tens, and the 1.1 tens. 13.9 tens is the same thing as
139. The fastest company prints 139
newspapers per minute. And 1.1 tens is the same thing as
11. The slowest company can only print
11 newspapers per minute.
We want to know how long it would
take the fastest and the slowest company to print 650 newspapers. To do that, we divide 650 by the
speed of printing. For the fastest company, we’ll have
650 divided by 139, which gives us 4.6762 continuing. And for the slowest company, we
divide 650 by 11, and we get 59.09 repeating. Our missing value of 𝑘 will be the
difference between the slowest time and the fastest time.
We can round the slowest time to 59
minutes, and we can round the fastest time to five minutes. The difference between the fastest
time and the slowest time is then 59 minus five, 54 minutes. It took the slower printing company
54 minutes longer than the fastest printing company to print 650 newspapers. And that’s option A.
Be careful of option B. In our first step, when we were
identifying the speed, we had 13.9 tens and 1.1 tens. If you did not convert these
values, if you didn’t change 13.9 tens to 139 and 1.1 tens to 11, then you would’ve
gotten a value that was 100 off. You would have gotten a difference
of 540 instead of 54. So, a key step here is checking the
units that we’re given in the speed on the graph for a final answer of 54.