The difference of two integers is 6. The sum of twice the smaller and the larger is 72. Find the integers.

The sum of 3 times a larger integer and 2

my answer the lager integer is 192 and the smaller integer is 72

x-y = 6

x + 2y = 72
subtract them:
3y = 66
y = 22
then
x-22 = 6
x = 28

the two numbers are 22 and 28

so "the sum of 3 times the larger and 2"
= 3(28) + 2 = 86

You claim your answer is:
192 and 72
Is their difference equal to 6 ????

12 and 6

Let's represent the two integers as x and y, where x is the smaller integer and y is the larger integer.

From the problem statement, we have two equations:

1) y - x = 6 (the difference of two integers is 6)
2) 2x + y = 72 (the sum of twice the smaller integer and the larger integer is 72)

To solve this system of equations, we can use the method of substitution.

From equation 1, we can rewrite it as y = x + 6.

Substituting this value of y in equation 2, we get:

2x + (x + 6) = 72
Simplifying the equation:

3x + 6 = 72
Subtracting 6 from both sides:

3x = 66
Dividing both sides by 3:

x = 22

Now, substitute this value of x into equation 1 to determine y:

y = x + 6
y = 22 + 6
y = 28

So, the smaller integer is 22 and the larger integer is 28.

To solve this problem, let's assign variables to the two integers. Let's call the smaller integer "x" and the larger integer "y".

According to the given information, the difference of two integers is 6. This can be written as:

y - x = 6 (Equation 1)

Also, the sum of twice the smaller and the larger is 72. This can be written as:

2x + y = 72 (Equation 2)

Now we have a system of two equations. We can solve this system using the method of substitution or elimination.

Let's solve it using the substitution method:

1. Solve Equation 1 for "y":
y = x + 6

2. Substitute the value of "y" in Equation 2:
2x + (x + 6) = 72

3. Simplify the equation:
3x + 6 = 72

4. Subtract 6 from both sides:
3x = 66

5. Divide both sides by 3:
x = 22

Now we have found the value of the smaller integer, which is 22.

To find the larger integer, substitute the value of "x" into Equation 1:
y - 22 = 6

Add 22 to both sides:
y = 28

So, the larger integer is 28 and the smaller integer is 22.

Therefore, the correct answer is that the larger integer is 28 and the smaller integer is 22.