A man purchased 20 tickets for a total of $225. The tickets cost $15 for adults and $10 for children

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A man purchased 20 tickets for a total of $225. The tickets cost $15 for adults and $10 for children. What was the cost of each ticket?

Declare variables:

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

Cost = Price * Quantity

We're given two equations:

1. a + c = 20
2. 15a + 10c = 225

Rearrange equation (1) in terms of a:

1. a = 20 - c
2. 15a + 10c = 225

Now that I have equation (1) in terms of a, we can substitute into equation (2) for a:
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