Question

Two families go skiing on a Saturday. Together, they spend $95 on pizza at a local restaurant and $65.73 for breakfast. One family purchases two adult lift tickets and four youth lift tickets for $166. Another family purchases four adult lift tickets and five youth lift tickets for $263. How much would it cost two adults and five kids to ski for a day?

Answer 1

$189

Explanation:

We can create a system of equations to solve this equation. They are as follows:

`2A + 4Y = 166\\4A + 5Y = 263`

In this case, I used "A" to represent adult lift tickets and "Y" to represent youth lift tickets.

We need to get one of the variable (A or Y) by itself in one of the equations. I am going to use the first equation.

`2A = -4Y + 166\\A = -(4)/(2)Y + (166)/(2) \\A = -2Y + 83`

Now that we have A by itself we can plug it into the second equation.

`4(-2Y + 83) + 5Y = 263\\-8Y + 332 + 5y = 263\\-3Y + 332 = 263\\-3Y = -69\\Y = 23`

We have found Y now lets plug it back into the first equation to find the value of A.

`2A + 4(23) = 166\\2A + 92 = 166\\2A = 74\\A = 37`

Let's check our variables by plugging them both in to the second equation.

`4(37) + 5(23) = 263\\148 + 115 = 263\\263 = 263`

Lastly, we can find out how much it would cost 2 adults and 5 kids to ski for a day, using this equation:

`2A + 5Y = ?\\\\2(37) + 5(23) = ?\\\\74 + 115 = 189\\`

Therefore, 2 adult tickets and 5 kid tickets would cost $189.

Hope this helps!!

- Kay :)

If you have any questions feel free to ask!