Question

The table below shows the ratios of black to white keys on pianos of various sizes.

Black A 27 54 81
White 13 B 78 C


Determine which table has the correct values for A, B, and C.

Black 8 27 54 81
White 13 40 78 119

Black 9 27 54 81
White 13 52 78 104

Black 9 27 54 81
White 13 39 78 117

Black 18 27 54 81
White 13 26 78 130

Answer 1

Black 9 27 54 81

White 13 39 78 117

Explanation:

Lets look at the first column in this table:

Black 9 27 54 81

White 13 39 78 117

How do we get from 9 to 13? In other words what do you multiply by 9 to get to 13? Set an equation to solve for x:

9x = 13

x = 13/9

Now lets look at the second column and see if this is true:

Black 9 27 54 81

White 13 39 78 117

27 × 13/9 = 39

Looking at the third column:

Black 9 27 54 81

White 13 39 78 117

54 × 13/9 = 78

Looking at the fourth column:

Black 9 27 54 81

White 13 39 78 117

81 × 13/9 = 117

This table works for values A, B and C as they have the same common ratio, 13/9