On a joint income tax​ return, Elizabeth​ Morrell's adjusted gross income was ​$3,7613,761 more than her husband​ Dan's adjusted gross income. Their combined adjusted gross income was ​$55,27755,277. Find Elizabeth​ Morrell's adjusted gross income.

Answer 1

Let's denote Dan's adjusted gross income as \( D \) and Elizabeth's adjusted gross income as \( E \).

From the information given, we can set up the following equations:

1. \( E = D + 3,761 \) (Elizabeth's income is $3,761 more than Dan's)
2. \( E + D = 55,277 \) (Their combined income)

We can substitute the first equation into the second equation:

\[ (D + 3,761) + D = 55,277 \]

Combining like terms, we get:

\[ 2D + 3,761 = 55,277 \]

Next, we will isolate \( D \) by subtracting \( 3,761 \) from both sides:

\[ 2D = 55,277 - 3,761 \]

Calculating the right side:

\[ 2D = 51,516 \]

Now, we divide by 2 to find \( D \):

\[ D = \frac{51,516}{2} = 25,758 \]

Now that we have \( D \), we can find \( E \):

\[ E = D + 3,761 = 25,758 + 3,761 = 29,519 \]

Therefore, Elizabeth Morrell's adjusted gross income is \( \boxed{29,519} \).