three numbers in the ratio of 7:3:2 have a sum of 228. what is the difference between the smallest and the largest numbers?
127
7 x + 3 x + 2 x = 228
To find the difference between the smallest and largest numbers in the given ratio, we first need to determine the values of those numbers. Here's how we can solve it step-by-step:
Step 1: Set up the ratio equation
Let's assume that the three numbers in the ratio are 7x, 3x, and 2x, where x is a common factor. The sum of these three numbers is 228, so we can write the equation as:
7x + 3x + 2x = 228
Step 2: Simplify the equation
Combine like terms on the left side of the equation:
12x = 228
Step 3: Solve for x
Divide both sides of the equation by 12:
x = 228 / 12
x = 19
Step 4: Calculate the values of the three numbers
Now that we have the value of x, we can find the values of the three numbers:
Smallest number = 2x = 2 * 19 = 38
Middle number = 3x = 3 * 19 = 57
Largest number = 7x = 7 * 19 = 133
Step 5: Find the difference between the smallest and largest numbers
To find the difference, subtract the smallest number from the largest number:
Difference = Largest number - Smallest number
Difference = 133 - 38
Difference = 95
Therefore, the difference between the smallest and largest numbers is 95.