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Question
The sum of two whole numbers is 18 and their product is 45, the numbers are ______.
Options
15 and 3
– 15 and – 3
– 15 and 3
15 and – 3
Solution
The sum of two whole numbers is 18 and their product is 45, the numbers are 15 and 3.
Explanation:
Let the two whole numbers are x and 18 – x and their product is 45.
∴ x(18 – x) = 45
`\implies` 18x – x2 = 45
`\implies` x2 – 18x + 45 = 0
`\implies` x2 – 3x – 15x + 45 = 0
`\implies` x(x – 3) – 15(x – 3) = 0
`\implies` (x – 3)(x – 15) = 0
Either x – 3 = 0 or x – 15 = 0
`\implies` x = 3 or x = 15
`\implies` x = 3 or 15
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