Question

Hurry please Brianna's family bought 7 tickets to an amusement park for $202. If Adult tickets were $34 and youth tickets were $22, how many adult tickets and how many youth tickets did her family buy? A. 2 adult tickets and 5 youth tickets B. 4 adult tickets and 3 youth tickets C. 5 Adult ticket and 2 youth tickets D. 3 Adult tickets and 4 youth tickets

Answer 1

The total tickets bought is 7 and they spent $202

Each adult ticket costs $34 and each youth ticket costs $22

Let "x" be the number of adult tickets and "y" be the number of youth tickets.

You can calculate the total number of tickets as

`x+y=7`

And the total amounf of the purchase as the number of adults tickets multiplied by its price (34x) plus the number of youth tickets multiplied by its price (22y)

`34x+22y=202`

Now we have an equation system determined and can calculate the values of x and y.

1) Write the first equation in terms of one of the variables, for example in terms of x

`\begin{gathered} x+y=7 \\ x=7-y \end{gathered}`

Next replace that expression in the second equation and calculate the value of y

`\begin{gathered} 34x+22y=202 \\ 34(7-y)+22y=202 \end{gathered}`

Solve the multiplication by applying the distributive propperty of multiplication

`\begin{gathered} 34\cdot7-34\cdot y+22y=202 \\ 238-34y+22y=202 \\ 238-12y=202 \end{gathered}`

Pass 238 to the other side of the equation by applying the inverse operation to both sides of it, i.e. "238" is positive, so you have to subtract it

`\begin{gathered} 238-238-12y=202-238 \\ -12y=-36 \end{gathered}`

Divide both sides of the equation by -12 to get the value of y

`\begin{gathered} -(12y)/(-12)=-(36)/(-12) \\ y=3 \end{gathered}`

With this value calculate x as:

`\begin{gathered} x=7-y \\ x=7-3 \\ x=4 \end{gathered}`

They bought 4 adult tickets and 3 youth tickets (Answer B.)