Help Please! The LCM of two numbers is 60. The GCF of the numbers is 5. One number is 5 more than the other. The numbers are________ and __________ Please help clueless in Massachusetts
60*5 = x(x+5)
x^2 + 5x - 300 = 0
x = 15
The two numbers are 15,20
To find the two numbers, we need to break down the problem into smaller steps.
Step 1: Find the prime factors of 60.
To find the prime factors of 60, we divide it by prime numbers until we can't divide anymore.
60 ÷ 2 = 30
30 ÷ 2 = 15
15 ÷ 3 = 5
The prime factors of 60 are 2, 2, 3, and 5.
Step 2: Use the GCF (Greatest Common Factor) of 5 to find the common factors of the two unknown numbers.
Since the GCF of the two numbers is 5, it means both numbers have factors of 5. We don't know the specific numbers yet, so we'll call them "5x" and "5y."
Step 3: Set up an equation based on the given information.
According to the problem, one number is 5 more than the other. So we can set up an equation based on this information:
5x = 5y + 5
Step 4: Solve the equation to find the values of x and y.
Now we can solve the equation to find the values of x and y:
We can divide the equation by 5 to simplify it:
x = y + 1
Step 5: Plug the values back into the equation to find the two numbers.
Since we represented the numbers as 5x and 5y, we can substitute the values of x and y back into the equation:
First number = 5x = 5(y + 1) = 5y + 5
Second number = 5y
So, the two numbers are 5y + 5 and 5y.
Since we don't have any additional information about the specific values of x and y, we can express the numbers in terms of "y."