A medical examiner in a school
created the given scatterplot to examine the relationship between the heights and
weights of nine different students. Which of the labeled points
represents the student with the greatest weight-to-height ratio?
The location along the 𝑥-axis will
give us the height of these students. And the location along the 𝑦-axis
will give us the weight of the students. And we need to calculate
weight-to-height ratios for the points labeled 𝐴, 𝐵, 𝐶, and 𝐷. First, we’ll consider these ratios
in fraction form, with the weight as the numerator and the height as the
denominator. Let’s start with student 𝐴. The weight is 80 kilograms. And the height falls a little bit
less than halfway between 155 and 160. So we could say it’s about 157
centimeters. And the weight-to-height ratio for
student 𝐴 is 80 over 157.
We follow the same procedure for
student 𝐵. The weight here, 85 kilograms. The height would fall a little bit
less than halfway between 175 and 180, but slightly closer to 175. And so we could call it 176. Now, student 𝐶 has a weight of 75
kilograms and a height that is just a bit more than 170 centimeters. And so we’ll say 171
centimeters. And finally, option 𝐷 is a student
with the weight of 90 kilograms and a height that is exactly halfway between 185
centimeters and 190 centimeters, which would be 187 and a half, 187.5.
Now, the student with the greatest
weight-to-height ratio is not the student that has the greatest weight. We have to be careful when we try
to compare these ratios. We don’t just look at the
numerator, because each of these fractions, each of these ratios, have a different
denominator. If we wanted to compare them as
fractions, we would have to find a common denominator. And since these numbers are so
large, it’s not an easy task to find a common denominator for these four values.
Instead, we can compare by
converting these fractions into decimals. We do this by dividing the
numerator by the denominator. 80 divided by 157 equals 0.5095
continuing. 85 divided by 176 equals 0.4829
continuing. 75 divided by 171 equals 0.4385
continuing. And 90 divided by 187.5 is exactly
0.48. Since we’re looking for the
greatest weight-to-height ratio, we’re interested in the largest decimal value. 0.5095 continuing is the greatest
decimal value. It has a five in the tenths
place. The other three ratios have a four
in the tenths place.
Since student 𝐴 has the highest
decimal value, 80 over 157 is the greatest weight-to-height ratio of the four
labeled points. It means that student 𝐴 has the
greatest weight-to-height ratio of the four labeled points.