The middle number is 3x the smaller number. The largest number is 6x the middle number. The sum of all three numbers is 34.

Answer 1

Let's use the variable y to represent the smallest number.

Then we can write the following expression to represent the middle number: 3y

We can write the following expression to represent the largest number: 6 • (3y) = 18y

Now we can write and solve the following equation since the sum of the three numbers is 34:

Smallest number + middle number + largest number = 34

y + 3y + 18y = 34

Now combine like terms and use inverse operations to solve for the value of y:

y + 3y + 18y = 34

22y = 34

22y / 22 = 34 / 22

y= 34/22 or 17/11

The smallest number is 17/11

The middle number will be 3 times the smaller or 51/11

The largest number will 18 times the smallest or 306/11

To verify that the sum is 34:

17/11 + 51/11 + 306/ 11 = 374/11

374/11 is equivalent to 34.