Charlie's age is 23 of Charlotte's age now. 2 years ago, the ratio of Charlie's age to Charlotte's age was 3 : 5. How old is Charlotte now?

To solve this problem, we can use the method of solving systems of linear equations.

Step 1: Let's denote Charlie's age as C and Charlotte's age as Ch. From the problem, we know that C = 2/3 * Ch.

Step 2: We also know that 2 years ago, the ratio of Charlie's age to Charlotte's age was 3:5. So, (C-2)/(Ch-2) = 3/5.

Step 3: Now we have a system of two equations, and we can solve it.

First, let's substitute C from the first equation into the second one:

(2/3*Ch - 2) / (Ch - 2) = 3/5.

Step 4: To simplify this equation, we can multiply both sides by 5 and by (Ch - 2):

5 * (2/3*Ch - 2) = 3 * (Ch - 2).

Step 5: Simplify the equation:

10/3*Ch - 10 = 3Ch - 6.

Step 6: To solve for Ch, we can first multiply every term by 3 to get rid of the fraction:

10Ch - 30 = 9Ch - 18.

Step 7: Then, we can subtract 9Ch from both sides:

Ch = 12.

So, Charlotte is 12 years old now.

Step 8: To find Charlie's age, we can substitute Ch = 12 into the first equation:

C = 2/3 * 12 = 8.

So, Charlie is 8 years old now.