Declare variables:

- Let a be the number of adult's tickets
- Let c be the number of children's tickets

We're given two equations:

- a + c = 20
- 15a + 10c = 225

- a = 20 - c
- 15a + 10c = 225

15(20 - c) + 10c = 225

Solve for

*c*in the equation 15(20 - c) + 10c = 225

We first need to simplify the expression removing parentheses

Simplify 15(20 - c): Distribute the 15 to each term in (20-c)

15 * 20 = (15 * 20) = 300

15 * -c = (15 * -1)c = -15c

Our Total expanded term is 300-15c

Our updated term to work with is 300 - 15c + 10c = 225

We first need to simplify the expression removing parentheses

Our updated term to work with is 300 - 15c + 10c = 225

**Step 1: Group the c terms on the left hand side:**

(-15 + 10)c = -5c

**Step 2: Form modified equation**

-5c + 300 = + 225

**Step 3: Group constants:**

We need to group our constants 300 and 225. To do that, we subtract 300 from both sides

-5c + 300 - 300 = 225 - 300

**Step 4: Cancel 300 on the left side:**

-5c = -75

**Step 5: Divide each side of the equation by -5**

-5c/-5 = -75/-5

c =

**15**

Recall from equation (1) that a = 20 - c. So we substitute c = 15 into this equation to solve for a:

a = 20 - 15

a =

**5**