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.
74/2 = 37
How about 36 and 38?
2/74=37
37-2=35(the age of the younger friend)
37+2=39(the age of the older friend)
39+35=74
To find the age of the older friend, we can set up a system of equations based on the given information.
Let's assume the age of the older friend is x years, and the age of the younger friend is y years.
From the first statement, "The difference between the ages of two friends is 2 years," we can write an equation:
x - y = 2
From the second statement, "The sum of their ages is 74 years," we can write another equation:
x + y = 74
Now we have a system of two equations:
x - y = 2
x + y = 74
We can solve this system using the method of substitution or elimination. Let's use the method of elimination:
Adding the two equations together, we get:
(x - y) + (x + y) = 2 + 74
2x = 76
x = 38
Now we know that the older friend is 38 years old.