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Question
Here is a key board of a harmonium:
- Find the ratio of white keys to black keys on the keyboard.
- What is the ratio of black keys to all keys on the given keyboard.
- This pattern of keys is repeated on larger keyboard. How many black keys would you expect to find on a keyboard with 14 such patterns.
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Solution
According to the given figure,
a. The total number of black keys = 7
The total number of white keys = 10
Hence, the ratio of white keys to black keys on the keyboard = `10/7`
b. The total number of all keys = 10 + 7 = 17
The ratio of black keys to all keys on the given keyboard = `7/17`
c. Black keys in 1 keyboard = 7
Black keys in 14 such keyboards = 14 × 7 = 98 keys.
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