Question

A

B
The table displays the wages that 4 students earned at their part-time jobs. For which student do the hours worked and wages earned represent a
PROPORTIONAL relationship?
C
4x D
Student C
Student D
Student A
Student A
Student B
Wages
Hour 1 Hour 2 Hour 3 Hour 4
Hour 5 Hour 6 Hour 7 Hour 8
$7
$12 $19
$24
$31
$38
$42
$49
$12
$18
$24
$30
$36 $42 $48
$5
$15 $15 $30 $30 $45 $45
$4
$9
$16 $25 $36 $49 $64
Student B
$6
Student C $5
Student D $1

Answer 1

Explanation:

A proportional relationship between two variables exists if they are related in a constant ratio. To determine which student has a proportional relationship between hours worked and wages earned, we need to check if the ratio of the hours worked to the wages earned is the same for all students.

Let's calculate the ratios for each student:

For Student A, the ratio is 1:7, 2:12, 3:19, 4:24, 5:31, 6:38, 7:42, 8:49. The ratios are not the same, so Student A does not have a proportional relationship.

For Student B, the ratio is 1:6, 2:12, 3:18, 4:24, 5:30, 6:36, 7:42, 8:48. The ratios are the same (1:6), so Student B has a proportional relationship.

For Student C, the ratio is 1:5, 2:15, 3:15, 4:30, 5:30, 6:45, 7:45, 8:?. The ratios are not the same, so Student C does not have a proportional relationship.

For Student D, the ratio is 1:4, 2:9, 3:16, 4:25, 5:36, 6:49, 7:64, 8:?. The ratios are not the same, so Student D does not have a proportional relationship.

Therefore, only Student B has a proportional relationship between hours worked and wages earned.