Answer:
Explanation:
Let's call the smaller number "x" and the larger number "y". Then we can translate the problem statement into equations:
"The product of two numbers is 132" can be written as: xy = 132
"3 times the smaller number plus 3 is equal to the bigger number minus 1" can be written as: 3x + 3 = y - 1, or equivalently, 3x = y - 4
We can now use substitution to solve for one of the variables. From the second equation, we have y = 3x + 4. Substituting this into the first equation, we get:
xy = 132
x(3x + 4) = 132
3x^2 + 4x - 132 = 0
We can now solve for x using the quadratic formula:
x = (-4 ± sqrt(4^2 - 4(3)(-132))) / (2(3))
x = (-4 ± sqrt(1756)) / 6
We only need the positive solution, since we're looking for a positive number, so:
x = (-4 + sqrt(1756)) / 6
x ≈ 5.046
Now that we know x, we can use either of the two equations we wrote earlier to solve for y. Let's use y = 3x + 4:
y = 3x + 4
y = 3(5.046) + 4
y ≈ 19.138
Therefore, the two numbers are approximately x = 5.046 and y = 19.138.