A family of five, two adults and threee children, purchased tickets to Luna Park. An adult ticket is more than a shild ticket.

The total cost of the tickets is .
Find the price of an adult ticket and a child ticket, showing all working.

Question

A family of five, two adults and threee children, purchased tickets to Luna Park. An adult ticket is

more than a shild ticket.

The total cost of the tickets is

.
Find the price of an adult ticket and a child ticket, showing all working.

UpStudy AI · Accepted Answer

Let the price of a child ticket be $$ x $$ dollars. Then, the price of an adult ticket would be $$ x + 10 $$ dollars.

The family consists of two adults and three children, so the total cost of the tickets can be expressed as:

$$
\text{Total cost} = 2 \times (\text{price of adult ticket}) + 3 \times (\text{price of child ticket})
$$

Substituting the expressions for the prices of the tickets, we have:

$$
\text{Total cost} = 2 \times (x + 10) + 3 \times x
$$

Now, we can simplify this expression:

$$
= 2(x + 10) + 3x
$$
$$
= 2x + 20 + 3x
$$
$$
= 5x + 20
$$

According to the problem, the total cost of the tickets is $$ 310 $$ dollars. Therefore, we can set up the equation:

$$
5x + 20 = 310
$$

Next, we will solve for $$ x $$:

1. Subtract $$ 20 $$ from both sides:

$$
5x = 310 - 20
$$
$$
5x = 290
$$

2. Divide both sides by $$ 5 $$:

$$
x = \frac{290}{5}
$$
$$
x = 58
$$

Now that we have found $$ x $$, which is the price of a child ticket, we can find the price of an adult ticket:

$$
\text{Price of adult ticket} = x + 10 = 58 + 10 = 68
$$

Thus, the prices of the tickets are:

- Price of a child ticket: $$ \$ 58 $$
- Price of an adult ticket: $$ \$ 68 $$

To verify, we can calculate the total cost:

$$
\text{Total cost} = 2 \times 68 + 3 \times 58
$$
$$
= 136 + 174
$$
$$
= 310
$$

The calculations confirm that the total cost is indeed $$ 310 $$ dollars. Therefore, the final answer is:

- Price of an adult ticket: $$ \$ 68 $$
- Price of a child ticket: $$ \$ 58 $$Adult ticket: \$68, Child ticket: \$58.

Upstudy AI Solution