one number excceds another ny five, and their product is 66. Find the numbers.
To solve this problem, let's use algebra to find the two numbers.
Let's assume the first number is 'x.'
According to the problem, "one number exceeds another by five." So, the second number will be 'x + 5'.
The problem also states that "their product is 66." So, we have the equation:
x * (x + 5) = 66
Now, let's solve it step by step:
1. Expand the equation:
x^2 + 5x = 66
2. Subtract 66 from both sides:
x^2 + 5x - 66 = 0
3. Factor the quadratic equation:
(x + 11)(x - 6) = 0
4. Set each factor equal to zero and solve for x:
x + 11 = 0 or x - 6 = 0
If x + 11 = 0, then x = -11.
If x - 6 = 0, then x = 6.
Therefore, we have two potential solutions: x = -11 and x = 6.
Since the problem states that one number exceeds the other by five, we can discard the negative number. Hence, the two numbers are 6 and 6 + 5 = 11.
So, the numbers are 6 and 11.
x(x+5) = 66
solve as a quadratic equation
btw, it factors, think 11, -6