NumericalModerate3 marks
The difference of two natural numbers is 7 and their product is 450. Find the numbers.
Topic: Quadratic word problems
Previous-year question practice database
Answer
Exam answer
If x – 25 = 0 ⇒ x = 25, y = 25 – 7 = 18
Explanation
Let the numbers be x and y. According the given condition x – y = 7 ⇒ y = x – 7 [ x>y] ...(i) xy = 450 ...(ii) From (i) & (ii) x (x – 7) = 450 x – 7x – 450 = 0 x – 25x + 18x – 450 = 0
x(x – 25) + 18(x – 25)= 0 (x – 25) (x + 18) = 0 If x + 18 = 0 ⇒ x = – 18 it is not a natural number. If x – 25 = 0 ⇒ x = 25, y = 25 – 7 = 18 Thus, numbers 25 and 18.
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