three numbers are in the ratio 6:3:1, and the sum of these numbers is 420. If the first number is reduced by 50%, the second number is increased by 42, and the sum of the numbers remains the same, find the resulting ratio of the numbers.
6x+3x+x = 420
x=42
6*42/2 = 126
3*42+42 = 164
420-(126+164) = 130
126:164:130 = 61:82:65
I don't think this answer is correct because 3*42=126 than + 42 = 168 not 164
To find the resulting ratio of the numbers, we need to determine the new values of the numbers after the given changes.
Let's denote the three numbers as 6x, 3x, and x, since they are in the ratio 6:3:1.
According to the conditions, the sum of these three numbers is 420:
6x + 3x + x = 420
Simplifying the equation:
10x = 420
Dividing both sides by 10:
x = 42
Now that we have the value of x, we can determine the original numbers as follows:
First number = 6x = 6 * 42 = 252
Second number = 3x = 3 * 42 = 126
Third number = x = 42
Now, let's apply the given changes and calculate the new values:
- The first number is reduced by 50%, so the new value is 252 * (1 - 0.50) = 252 * 0.50 = 126.
- The second number is increased by 42, so the new value is 126 + 42 = 168.
- The third number remains the same at 42.
Now, we can find the resulting ratio by dividing each number by their greatest common divisor (GCD). The GCD of 126, 168, and 42 is 42.
Dividing each number by 42:
126 / 42 = 3
168 / 42 = 4
42 / 42 = 1
Therefore, the resulting ratio of the numbers is 3:4:1.