Two girls have $76 between them if the first gave the second $7 they would each have the same amount of money how much did each girls have

Let the amount of money the first girl has be $ x $, and the amount the second girl has be $ y $.

From the problem, we know:
1. $ x + y = 76 $ (the total amount of money is $76).
2. If the first girl gives the second girl $7, they would have the same amount of money. This gives the equation:
   \[
   x - 7 = y + 7
   \]

Now, let's solve this system of equations.

### Step 1: Solve the second equation for $ x $
From the second equation, we have:
\[
x - 7 = y + 7
\]
Add 7 to both sides:
\[
x = y + 14
\]

### Step 2: Substitute into the first equation
Now substitute $ x = y + 14 $ into the first equation $ x + y = 76 $:
\[
(y + 14) + y = 76
\]
Simplify:
\[
2y + 14 = 76
\]
Subtract 14 from both sides:
\[
2y = 62
\]
Divide by 2:
\[
y = 31
\]

### Step 3: Find $ x $
Substitute $ y = 31 $ back into $ x = y + 14 $:
\[
x = 31 + 14 = 45
\]

Thus, the first girl had $45, and the second girl had $31.

Would you like a more detailed explanation? Also, here are some related questions to explore:

1. What would happen if the first girl gave $10 instead of $7?
2. How can we solve similar problems with different total amounts of money?
3. What if instead of equal amounts, one had twice the money after the transaction?
4. Can we generalize this problem to work with any total amount?
5. How does changing the amounts exchanged impact the result?

**Tip:** When solving word problems, it's helpful to define variables clearly and set up equations that reflect the relationships described in the problem.

Two girls have $76 between them. If the first gave the second $7, they would each have the same amount of money. How much did each girl have?

Solve the algebra problem where two girls have $76 between them, and the first girl gives the second $7 to equalize their amounts. This step-by-step solution involves linear equations and is suitable for students in Grades 6-8.

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