The sum of two numbers is 20. One number is 3 times the other. Find the numbers.
x + 3x = 20
. . .
To solve this problem, let's break it down into steps:
Step 1: Define the variables
Let's assume that one of the numbers is x, and the other number is 3 times that number, so it will be 3x.
Step 2: Set up the equation
According to the problem, the sum of the two numbers is 20. So, we can write the equation as:
x + 3x = 20
Step 3: Simplify the equation
Combine like terms on the left side of the equation:
4x = 20
Step 4: Solve for x
To solve for x, we need to isolate it on one side of the equation. Divide both sides of the equation by 4:
x = 20 / 4
x = 5
Step 5: Find the other number
Now that we have found the value of x, we can find the other number by multiplying it by 3:
Other number = 3 * x
Other number = 3 * 5
Other number = 15
Step 6: Verify the solution
To verify our solution, we can substitute the values we found back into the original equation:
5 + 15 = 20
So, the two numbers are 5 and 15.