Tonya polled boys and girls in her grade to determine how many prefer math to other subjects. The results are shown in the table. Which is a true statement?
The table shows that 14 out of 30 boys prefer math and that 16 out of 32 girls prefer math
A. The relationship is proportional because 16-4=2 and 32-30=2
B. The relationship is proportional because 30-14 = 16 and 32-16 = 16
C. The relationship is not proportional because 14/16=7/8 and 30/32=15/16
D. Relationship is not proportional because 14/30= 17/15 and 16/32=1/2
Help please!!
proportions involve a comparison of ratios, so A and B are out
The ratio you are interested in is the
# who prefer math : total number
So, D
Better review the topic in your text
To determine if the relationship is proportional, we need to compare the ratios of boys who prefer math to the total number of boys, and girls who prefer math to the total number of girls.
For the boys, we have 14 out of 30 who prefer math, which can be written as 14/30. Simplifying this fraction gives us 7/15.
For the girls, we have 16 out of 32 who prefer math, which can be written as 16/32. Simplifying this fraction gives us 1/2.
Now we can compare the two ratios:
Boys: 7/15
Girls: 1/2
Option C states that the relationship is not proportional because 14/16 = 7/8 (referring to the fractions obtained by simplifying the ratios for boys and girls), and 30/32 = 15/16. But this is incorrect; 7/15 is not equal to 7/8, and 1/2 is not equal to 15/16.
Therefore, the correct answer is option D: The relationship is not proportional because 14/30 = 17/15 (boys ratio), and 16/32 = 1/2 (girls ratio). This shows that the ratios are not equal and, therefore, the relationship is not proportional.