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Question
The product of two successive integral multiples of 5 is 300. Determine the multiples.
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Solution
Given that the product of two successive integral multiples of 5 is 300.
Let the integers be 5x, and 5(x + 1)
Then, by the integers be 5x and 5(x + 1)
Then, by the hypothesis, we have
5x ∙ 5(x + 1) = 300
⇒ 25x (x + 1) = 300
⇒ 𝑥2 + 𝑥 = 12
⇒ 𝑥2 + 𝑥 - 12 = 0
⇒ 𝑥2 + 4𝑥 - 3𝑥 - 12 = 0
⇒ x(x + 4) -3(x + 4) = 0
⇒ (x + 4) (x – 3) = 0
⇒ x = -4 or x = 3
If x = -4, 5x = -20, 5(x + 1) = -15
x = 3, 5x = 15, 5(x + 1) = 20
∴ The two successive integral multiples are 15, 20 or -15, -20.
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