The difference between the ages of two friends is 2 years. The sum of their ages is 74 years. Find the age of the older friend.

Here's a clue:

74/2 = 37

x+y=74

x-y=2 (the y's cancel so...)
2x=76
x= 38
the older friend is 38, the other one is 36

Let's define the age of the older friend as x, and the age of the younger friend as y.

According to the problem, the difference in their ages is 2 years, so we can write:

x - y = 2 ----(1)

The sum of their ages is 74 years, so we can also write:

x + y = 74 ----(2)

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

Let's solve this system of equations using the method of substitution. We can express y in terms of x from equation (1):

y = x - 2

Substitute this expression for y into equation (2):

x + (x - 2) = 74

Simplifying the equation:

2x - 2 = 74

Add 2 to both sides of the equation:

2x = 76

Divide both sides by 2:

x = 38

Therefore, the age of the older friend is 38 years.

To find the age of the older friend, we can set up a system of equations using the given information.

Let's call the age of the older friend X, and the age of the younger friend Y.

According to the first statement, the difference between their ages is 2 years. This can be expressed as:

X - Y = 2 ...(Equation 1)

According to the second statement, the sum of their ages is 74 years. This can be expressed as:

X + Y = 74 ...(Equation 2)

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

Let's solve using the method of substitution:
1. Solve equation 1 for X in terms of Y:
X = 2 + Y

2. Substitute X in equation 2 with 2 + Y:
(2 + Y) + Y = 74

3. Simplify the equation:
2 + 2Y = 74

4. Subtract 2 from both sides:
2Y = 72

5. Divide both sides by 2:
Y = 36

Now that we have determined the age of the younger friend as 36, we can substitute this value back into equation 2 to find the age of the older friend:

X + 36 = 74

Subtract 36 from both sides:
X = 38

Therefore, the age of the older friend is 38 years.