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
The correct values for A, B, and C are:
A = 27
B = 52
C = 104
Therefore, the correct table is:
Black 9 27 54 81
White 13 52 78 104
To determine which table has the correct values for A, B, and C, we need to find the pattern in the ratios of black to white keys.
Looking at the ratio for A, it can be observed that A is three times the number of white keys. Therefore, A should be greater than 13 and divisible by 3. The only table that satisfies this condition is:
Black 9 27 54 81
White 13 39 78 117
Now, let's move on to determining the values for B and C. Looking at the ratio for B, it can be observed that B is twice the number of white keys. Therefore, B should be greater than 13 and divisible by 2. The only table that satisfies this condition is:
Black 9 27 54 81
White 13 39 78 117
Finally, looking at the ratio for C, it can be observed that C is three times the number of white keys minus 3. Therefore, C should be greater than 13 and divisible by 3, minus 3. The only table that satisfies this condition is:
Black 9 27 54 81
White 13 39 78 117
Therefore, the correct table is:
Black 9 27 54 81
White 13 39 78 117