Video Transcript
The given scatter plot shows the
print speed and cost per newspaper for 19 newspaper companies and the line of best
fit for the data. The line of best fit for the data
is given by the equation 𝑐 equals negative 2.44𝑠 plus 39.2, where 𝑐 is the cost
in cents per newspaper and 𝑠 is the printing speed in tens of newspapers per
minute. What is the best estimate for the
speed, in newspapers per minute, of a company that prints eight newspapers per
dollar?
This question is not difficult but
does require us to pay close attention to units. We’re given the line of best fit 𝑐
equals negative 2.44𝑠 plus 39.2, where 𝑐 represents cents per newspaper. That means 𝑐 will be the cost in
cents for every one newspaper printed. We know the company we’re
interested in prints eight newspapers for every dollar. We know that one dollar is 100
cents and that with 100 cents, this company can print eight newspapers. In order for us to use this as a 𝑐
value, we need to find out if it costs 100 cents to make eight newspapers, How many
cents does it cost to make one?
Eight divided by eight equals
one. And if we divide the denominator by
eight, we must divide the numerator by eight. 100 divided by eight equals 12 and
a half. That means that it costs 12 and a
half cents per newspaper printed at this company. And we can plug in 12 and a half
cents per newspaper as the 𝑐 value in the line of best fit, where we’ll say 12 and
a half is equal to negative 2.44𝑠 plus 39.2. To find out the speed in newspapers
per minute, we’ll first need to calculate the 𝑠 value. To do that, we subtract 39.2 from
both sides of the equation. 12 and a half minus 39.2 equals
negative 26.7. Negative. 26.7 is equal to negative 2.44
times 𝑠.
To find 𝑠, we need to divide both
sides of the equation by negative 2.44. Negative 26.7 divided by negative
2.44 equals positive 10.9426 continuing. And so we found 𝑠 equals 10.9426
continuing. But again, we need to be very
careful of our units because 𝑠 is the printing speed in tens of newspapers per
minute. And our question is looking for the
speed in newspapers per minute, not tens of newspapers per minute. If we round 10.9426 to the nearest
tenth, we get 10.9. We need to consider what 10.9 tens
of newspapers per minute would be in newspapers per minute. If we have 10.9 tens, that means
10.9 times 10. And so we could say we have 109
newspapers per minute.
Now, this is not the only way we
could have solved this question. If we go back to when we found 12.5
cents per newspaper, we could have then looked on our chart at 12.5 cents per
newspaper. Cents per newspaper is the
𝑦-axis. If we look at 12.5 along the
𝑦-axis, we see that this is between 10 and 12 along the 𝑥-axis. And the 𝑥-axis is the print speed
in tens of newspapers. If we estimate the coordinates of
this point to be 11, 12 and a half, then we would say that there are 11 tens of
newspapers per minute printed. And 11 tens would be equal to
110. 11 times 10 is 110. And the best estimate for that
would be 109 newspapers per minute.
