The product of two numbers is

Question

12. The sum of the larger number
and twice the smaller is 11. Find
the two numbers.
A. 4, 3
B. 8, 5/2


C. 3, 3/2


D. 3/2, -1

Answer 1

Let's assume the two numbers are x and y, with x being the larger number. We are given two equations:

1) xy = 12
2) x + 2y = 11

From equation 1, we can solve for y:
y = 12/x

Substituting this into equation 2, we get:
x + 2(12/x) = 11
x + 24/x = 11

Multiplying through by x to get rid of the fractions:
x^2 + 24 = 11x
x^2 - 11x + 24 = 0

Factoring the equation:
(x - 8)(x - 3) = 0

Setting each factor equal to zero and solving for x:
x - 8 = 0 --> x = 8
x - 3 = 0 --> x = 3

We have two possible values for x, so let's plug them back into equation 1 to find the corresponding values of y:

For x = 8:
y = 12/8 = 3/2

For x = 3:
y = 12/3 = 4

So the two possible pairs of numbers are (8, 3/2) and (3, 4).

Therefore, the correct answer is B. 8, 5/2.