Out of the numbers divisible by 3, we picked 4 consecutive numbers. To the sum of these, we added a third of the sum, and then the half of the third of the sum. We got 225. What are those 4 numbers?
Let x be the sum,
x*(1+1/3+1/6)=225
x=225*(6/9)=150=33+36+39+42
To find the four consecutive numbers that satisfy the given criteria, let's break down the problem step by step.
Step 1: Finding the sum of the four consecutive numbers
Let's assume the first number is x. Since the numbers are consecutive, the second, third, and fourth numbers will be x+1, x+2, and x+3, respectively. The sum of these four numbers is:
Sum = x + (x+1) + (x+2) + (x+3) = 4x + 6
Step 2: Adding a third of the sum to the previous result
We are given that we added a third of the sum calculated in the previous step to the sum. So, we write the equation:
Sum + (1/3)Sum = 225
Substituting the value of Sum from Step 1:
(4x + 6) + (1/3)(4x + 6) = 225
Simplifying the equation:
(12x + 18 + 4x + 6) = 675
16x + 24 = 675
16x = 675 - 24
16x = 651
x = 651/16
x ≈ 40.6875
Step 3: Calculating the four consecutive numbers
Now that we have the value of x, we can find the four consecutive numbers.
First number = x ≈ 40.6875
Second number = x + 1 ≈ 40.6875 + 1 ≈ 41.6875
Third number = x + 2 ≈ 40.6875 + 2 ≈ 42.6875
Fourth number = x + 3 ≈ 40.6875 + 3 ≈ 43.6875
Therefore, the four consecutive numbers that satisfy the given conditions are approximately 40.6875, 41.6875, 42.6875, and 43.6875.