Question 3 of 11beginner🔧 ApplyNumerical2 marks

Find two numbers whose sum is 27 and product is 182.

Correct Answer

The two numbers are 13 and 14.

Exercise: EXERCISE 4.2 | Q: 3 | (Page 7)
For More Understanding

Explanation

This is a standard word problem from Exercise 4.3 that requires forming a quadratic equation from given conditions. The student must define variables, form equations based on sum and product conditions, solve the resulting quadratic equation by factorization, and verify the answer. The context shows similar problems where variables are defined and quadratic equations are formed from word problems.

Solution Steps

  1. Step 1: Let one number be xx. Then the other number is (27−x)(27 - x) since their sum is 27.

  2. Step 2: According to the question, product of the numbers = 182. So, x(27−x)=182x(27 - x) = 182.

  3. Step 3: Simplifying: 27x−x2=18227x - x^2 = 182, which gives x2−27x+182=0x^2 - 27x + 182 = 0.

  4. Step 4: Solving by factorization: We need two numbers whose product is 182 and sum is 27. These numbers are 14 and 13.

  5. Step 5: So, (x−14)(x−13)=0(x - 14)(x - 13) = 0, which gives x=14x = 14 or x=13x = 13.

  6. Step 6: If x=14x = 14, other number = 27−14=1327 - 14 = 13. If x=13x = 13, other number = 27−13=1427 - 13 = 14.

  7. Step 7: Verification: Sum = 13+14=2713 + 14 = 27 and Product = 13×14=18213 \times 14 = 182. Hence, the two numbers are 13 and 14.

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