Question
This table represents equivalent ratios.
What are the values of a and b?
Responses
a = 6 , b = 12
a, = 6 , , b, = 12
a = 8 , b = 12
a, = 8 , , b, = 12
a = 6 , b = 15
a, = 6 , , b, = 15
I don't know.
I don't know.
x y
0.5 0.4
2 1.6
a 4.8
12 9.6
15 b
From the given table, we can see that the ratio of x to y remains constant as it progresses.
For the first row, we have x = 0.5 and y = 0.4. The equivalent ratio is 0.5/0.4 = 1.25.
For the second row, we have x = 2 and y = 1.6. The equivalent ratio is 2/1.6 = 1.25.
For the third row, we have x = a and y = 4.8. The equivalent ratio is a/4.8 = 1.25.
For the fourth row, we have x = 12 and y = 9.6. The equivalent ratio is 12/9.6 = 1.25.
For the fifth row, we have x = 15 and y = b. The equivalent ratio is 15/b = 1.25.
Since the ratio of x to y is constant in each row and it is equal to 1.25, we can solve for a and b by setting up and solving the following equations:
a/4.8 = 1.25
a = 1.25 * 4.8
a = 6
15/b = 1.25
15 = 1.25 * b
b = 15 / 1.25
b = 12
Therefore, the values of a and b are a = 6 and b = 12. So, the correct response is a = 6, b = 12.
Based on the information provided, the table represents equivalent ratios. The values of a and b are a = 6 and b = 15.
To find the values of a and b, we need to look for a pair of equivalent ratios in the table. Equivalent ratios are ratios that have the same value, even though the numbers may be different.
Looking at the table, we can see that the ratio 0.5:0.4 is equivalent to the ratio 12:9.6.
Therefore, a = 0.5 and b = 9.6.