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Question
Suppose 2 kg of sugar contains 9 × 106 crystals.
How many sugar crystals are there in
- 5 kg of sugar?
- 1.2 kg of sugar?
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Solution
i. Let the number of sugar crystals in 5 kg of sugar be x.
The given information, in the form of a table, is as follows:
| Amount of sugar (in kg) | 2 | 5 |
| Number of crystals | 9 × 106 | x |
The amount of sugar and the number of crystals it contains are directly proportional to each other. Therefore, we obtain
⇒ `2/(9xx10^6) = 5/x`
⇒ x = `(5xx9xx10^6)/2`
⇒ x = `(5xx9xx100000)/2`
⇒ x = 2.25 × 107
Hence, the number of sugar crystals is 2.25 × 107
ii. Let the number of sugar crystals in 1.2 kg of sugar be y. The given information, in the form of a table, is as follows:
| Amount of sugar (in kg) | 2 | 1.2 |
| Number of crystals | 9 × 106 | y |
⇒ `2/1.2 = (9xx10^6)/y`
⇒ `y = (1.2xx9xx10^6)/2`
⇒ y = 5.4 × 106
Hence, the number of sugar crystals is 5.4 x 106
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