Final answer:
To find the consecutive positive integers whose product, when the first is multiplied by three, equals 60, we set up and solve a quadratic equation, revealing that the integers are 4 and 5.
Step-by-step explanation:
Consecutive integers are integers that follow each other in sequence without any gaps. If you have one integer, the consecutive integers would be the ones that come directly before and after it.
For a given integer nn, the consecutive integers would be n−1n−1 and n+1n+1. So, if nn is any integer, then n−1n−1, nn, and n+1n+1 are consecutive integers.
To find two consecutive positive integers where 3 times the first number multiplied by the second number is 60, we can set up an equation. Let the first integer be x and the second integer be x+1.
The equation based on the given information is:
3x * (x + 1) = 60
Expanding this, we get:
3x^2 + 3x = 60
Subtracting 60 from both sides to set the equation to zero, we have:
3x^2 + 3x - 60 = 0
Divide everything by 3 to simplify:
x^2 + x - 20 = 0
Factoring the quadratic equation, we get:
(x + 5)(x - 4) = 0
This gives us two possible solutions for x, which are -5 and 4. Since we are looking for positive integers, we discard -5. So the first integer is 4 and the second consecutive integer is 5.
Checking the solution:
3 * 4 * 5 = 60,
which confirms that the integers 4 and 5 satisfy the given condition.