Question

The product of two whole numbers is 196 and their sum is 35. what are the two numbers

Answer 1

A) x * y = 196A) x = 196 / y

B) x + y = 35Substituting A) into B)
B) 196 / y + y = 35Multiplying both sides by y
B) 196 + y^2 = 35yB) y^2 -35y + 196 = 0
X1 = 28X2 = 7

Answer 2

The values of a and b which gives a product of 196 and a sum of 35 are 28 and 7

Let the two number be a and b :

Product of the two numbers :

• a × b = 196 - - - (1)

Sum of the two numbers :

• a + b = 35 - - - (2)

From (2) :

• a = 35 - b - - - (3)

Substituting (3) into (1)

(35 - b) × b = 196

35b - b² = 196

-b² + 35b - 196 = 0

b² - 35b + 196

Solving the quadratic equation

b² - 28b - 7b + 196 = 0

b(b - 28) - 7(b - 28) = 0

b = 28 or b = 7

From (3)

a = 35 - 28

a = 7

Therefore, the values of a and b are 28 and 7

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