Nancy is 4 years younger than Monica. Seven years from now the sum of their ages will be 82. How old are they know?

Now:

Monica's age ---- x
Nancy's age ---- x-4

seven years from now:
Monica ---- x+7
Nancy ----- x-4 + 7 = x + 3

so
x-4 + x+3 = 82

continue

N = M + 4

N + 7 + M + 7 = 82 ... N + M = 68

substituting ... M + 4 + M = 68

solve for M , substitute back to find N

equation should have been

x+7 + x+3 = 82

etc

correction for me too (must be contagious)

swap the N and M values
... Nancy is the younger one

To determine the present ages of Nancy and Monica, let's break down the problem into smaller steps:

Let's assume Nancy's age is represented by 'N'.
Since Nancy is 4 years younger than Monica, Monica's age can be represented as 'N + 4'.

According to the problem, seven years from now, the sum of their ages will be 82. Let's calculate their ages seven years from now:

Nancy's age seven years from now: N + 7
Monica's age seven years from now: (N + 4) + 7

According to the problem, the sum of their ages seven years from now will be 82, so we can summarize it as follows:

(N + 7) + [(N + 4) + 7] = 82

Now, let's solve the equation:

N + 7 + N + 4 + 7 = 82
2N + 18 = 82
2N = 82 - 18
2N = 64
N = 64/2
N = 32

So, Nancy's present age is 32 years.

Now, we can find Monica's age using the formula mentioned earlier:

Monica's age = Nancy's age + 4
Monica's age = 32 + 4
Monica's age = 36

Therefore, Nancy is currently 32 years old, and Monica is currently 36 years old.