Question

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?

Answer 1

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.