Ms. Rodriguez is comparing data about the number of leaf samples tested by three scientists in each of two laboratories. The tables show the number of leaf samples tested and the time spent testing.

Question

Laboratory A Laboratory B
Scientist Number of Leaf
Samples Tested Time Spent
(minutes) Scientist Number of Leaf
Samples Tested Time Spent
(minutes)
Steve 90 30 Mary 140 35
Jesmy 180 45 Brian 160 40
Buck 210 60 Kate 220 55

Which laboratory shows a proportional relationship between the number of leaf samples tested and the time spent testing?
A.
neither laboratory A nor laboratory B
B.
both laboratory A and laboratory B
C.
only laboratory B
D.
only laboratory A

Answer 1

To determine which laboratory shows a proportional relationship between the number of leaf samples tested and the time spent testing, we need to check if the ratio of leaf samples tested to time spent is consistent for each scientist in the laboratory.

For Laboratory A:

• Steve: \( \frac{90 \text{ samples}}{30 \text{ minutes}} = 3 \)
• Jesmy: \( \frac{180 \text{ samples}}{45 \text{ minutes}} = 4 \)
• Buck: \( \frac{210 \text{ samples}}{60 \text{ minutes}} = 3.5 \)

The ratios are not consistent (3, 4, and 3.5), so Laboratory A does not show a proportional relationship.

For Laboratory B:

• Mary: \( \frac{140 \text{ samples}}{35 \text{ minutes}} = 4 \)
• Brian: \( \frac{160 \text{ samples}}{40 \text{ minutes}} = 4 \)
• Kate: \( \frac{220 \text{ samples}}{55 \text{ minutes}} = 4 \)

The ratios for all scientists in Laboratory B are consistent (all equal to 4), indicating a proportional relationship.

Based on this analysis, the answer is:

C. only laboratory B