Three numbers add up to 180. The second number is twice the first, and the third number is three times the first. WHAT IS EACH NUMBER?
x+y+z = 180
y = 2x
z =3x
6x=180
x = 30
y=60
z=90
To solve this problem, we can break it down into smaller steps:
Step 1: Identify the variables
Let's assign variables to the numbers given in the problem. Let:
- First number = x
- Second number = 2x (twice the first number)
- Third number = 3x (three times the first number)
Step 2: Set up the equation
According to the problem statement, the three numbers add up to 180. So we can write the equation:
x + 2x + 3x = 180
Step 3: Simplify the equation
Combine like terms on the left side of the equation:
6x = 180
Step 4: Solve for x
Divide both sides of the equation by 6 to isolate x:
x = 180 / 6
x = 30
Step 5: Find the other numbers
Now that we have found the value of x, we can substitute it back into the variables to find the second and third numbers:
Second number = 2x = 2 * 30 = 60
Third number = 3x = 3 * 30 = 90
Step 6: Check the answer
To verify if our solution is correct, we can add up the three numbers:
30 + 60 + 90 = 180
The sum is indeed 180; therefore, our solution is correct.
So, the three numbers are:
First number = 30
Second number = 60
Third number = 90
Let's solve this step-by-step.
Let's represent the first number as 'x'.
According to the given information:
1. The second number is twice the first => Second number = 2x
2. The third number is three times the first => Third number = 3x
We know that the sum of all three numbers is 180, so we can set up the equation:
x + 2x + 3x = 180
Combining like terms:
6x = 180
Dividing both sides by 6:
x = 30
Now, let's substitute the value of x into the expressions for the second and third numbers:
Second number = 2x = 2 * 30 = 60
Third number = 3x = 3 * 30 = 90
So, the three numbers are:
First number = 30
Second number = 60
Third number = 90