Three even numbers sum up to 126. The smallest is half the largest and the middle number is 3/5 the largest. What are the 3 numbers?
Let's call the largest even number "x".
According to the problem, the smallest even number is half the largest, so we can write:
smallest = x/2
The middle even number is 3/5 the largest, so we can write:
middle = (3/5)x
We know that the sum of the three even numbers is 126, so we can write:
smallest + middle + largest = 126
Substituting the expressions we found for smallest and middle, we get:
x/2 + (3/5)x + x = 126
To solve for x, we can simplify the left side of the equation by finding a common denominator:
5x/10 + 6x/10 + 10x/10 = 126
Combining like terms, we get:
21x/10 = 126
Multiplying both sides by 10/21, we get:
x = 60
So the largest even number is 60.
Using the expressions we found for smallest and middle, we can find the other two even numbers:
smallest = x/2 = 30
middle = (3/5)x = 36
Therefore, the three even numbers are 30, 36, and 60.