**Step 1: Define your variables.**

#of adult tickets = x

# of kids tickets = y

**Step 2: What do you know?**

The number of kids tickets added to the number of adult tickets is equal to the total number of tickets. This can be expressed as:

x + y = 275

Great! But that's not incredibly useful all by itself. What else do you know? The total money made (1025$) will be equal to the money made from adult tickets plus the money made from kids tickets.

(3$ * y) + (5$ * x) = 1,025$ ...........simplify

3y + 5x = 1025

These equations each have two variables! To solve for a variable, you need an equation with just
one variable.

**Step 3: Solve for x relative to y.**

Starting with your simplest equation, determine the value of one of your variables. We'll find x.

x + y = 275

x = 275 - y

This allows us to combine our equations.

**Step 4: Combine equations. **

Now you know what x is relative to y. You can plug this new value into your second equation.

3y + 5x = 1,025

3y + 5(275 - y) = 1,025

**Step 5: Solve for y.**

Your new and improved situation only has one variable. This means you can solve it.

3y + 5(275 - y) = 1,025 -------- distribute the 5

3y + 1375 - 5y = 1,025 --------- simplify the variable numbers

-2y + 1375 = 1,025 ------------ subtract the whole number

-2y = -350 ----------------------- divide by y

y = 175

**Step 6: Solve for x.**

Now that we know what y is, we can plug it back into the simple equation to find x.

x + y = 275

x + 175 = 275

x = 100

So now we have both variables.

x = 100

y = 175

Recall what our variables represent, and you have your answer. There are
100 adult tickets, and 175 kids tickets sold.

This method of combining equations to solve one variable at a time is useful whenever you have multiple equations with the same variables.