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

1 answer

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.