Question

There are two numbers, S is the smaller number, L is the larger number. The sum of the

smaller number and three times the larger number is 19. Also, when the square of the larger
number is increased by twice the smaller number, the result is 33. What are the two numbers?

Answer 1

Larger number is 5 and Smaller number is 4

Explanation:

We know larger number is L and smaller number is S

1st Equation:

S + 3L = 19

S = 19 - 3L -----> ( i)

2nd Equation:

L^2 + 2S = 33

*Putting value of S from Equation ( i)

L^2 + 2(19 - 3L) = 33

L^2 + 38 - 6L - 33 = 0

L^2 - 6L + 5 = 0

*Using mid term factorization*

L^2 -(5L + L) + 5 = 0

L^2 - 5L - L + 5 = 0

*Taking Common*

L( L - 5) -1(L-5) = 0

* again taking common*

(L-5) (L-1) = 0

Either, or,

L-5 = 0 L - 1 = 0

L = 5 L = 1

From Equation (i) From Equation (i)

S = 19 - 3L S = 19 - 3L

S = 19 - 3 × 5 S = 19 - 3

S = 19 - 15 S = 16 ( this answer is rejected because L

S = 4 should be greater)

therefore greater number is 5 and smaller number is 4