The difference between two natural numbers is 6.adding 10 to the twice of the larger number,we get 2 less than 3 times of the smaller number.find these numbers.

let the smaller number be x. Then the larger number will be x+6. Now according to the question;

2(x+6) +10=3x-2
2x+ 12+ 10=3x-2
3x-2x=12+10+2
x=24 and the larger number will be (24+6)=30.

smaller ----- x

larger ------ x+6

Just translate the English into Math:

2(6+x) + 10 = 3x - 2

solve for x

Excellent . Keep it up .

To solve this problem, let's use algebra.

Let's assume the smaller number is x and the larger number is y.

From the given information, we know that y - x = 6. This means the difference between the two numbers is 6.

Next, we're told that by adding 10 to twice the larger number, we get 2 less than 3 times the smaller number. We can write this as an equation:

2y + 10 = 3x - 2

Now, we have a system of two equations:

y - x = 6 (Equation 1)
2y + 10 = 3x - 2 (Equation 2)

To solve this system, we can rearrange Equation 1 to get y = x + 6 and substitute it into Equation 2:

2(x + 6) + 10 = 3x - 2

Simplifying this equation, we have:

2x + 12 + 10 = 3x - 2
2x + 22 = 3x - 2
22 + 2 = 3x - 2x
24 = x

So, the smaller number (x) is 24.

Now, substituting this value of x into Equation 1:

y - 24 = 6
y = 6 + 24
y = 30

Therefore, the larger number (y) is 30.

In conclusion, the smaller number is 24 and the larger number is 30.