Question

POSSIBLE POINTS: 15The Gonzalez family attended a concert and visited an art museum. Concert tickets were $24.75 for adults and $16.00 for children, for a total cost of$171.75. Museum tickets were $8.25 for adults and $4.50 for children, for a total cost of $54.75. How many adults and how many children are inthe Gonzalez family?

Answer 1

Number of adults: x

Number of children: y

Concert tickets:

$24.75 for 1x

$16.00 for 1y

Total: $171.75

`24.75x+16.00y=171.75`

Museum tickets:

$8.25 for 1x

$4.50 for 1y

Total: $54.75

`8.25x+4.50y=54.75`

To find the number of adults and chidren use the next system of equations:

`\begin{gathered} 24.75x+16.00y=171.75 \\ 8.25x+4.50y=54.75 \end{gathered}`

Solve x in the first equation:

`\begin{gathered} 24.75x=171.75-16.00y \\ x=(171.75)/(24.75)-(16.00y)/(24.75) \end{gathered}`

Substitute the x in the second equation for the value you get above:

`8.25((171.75)/(24.75)-(16.00y)/(24.75))+4.50y=54.75`

Solve y:

`\begin{gathered} 57.25-(132y)/(24.75)+4.50y=54.75 \\ \\ -(132y)/(24.75)+4.50y=54.75-57.25 \\ \\ (-132y+111.375y)/(24.75)=-2.5 \\ \\ -132y+111.375y=-2.5(24.75) \\ -20.625y=-61.875 \\ y=(-61.875)/(-20.625) \\ \\ y=3 \end{gathered}`

Use the value of y= 3 to solve x:

`\begin{gathered} x=(171.75)/(24.75)-(16.00(3))/(24.75) \\ \\ x=(171.75)/(24.75)-(48)/(24.75) \\ \\ x=(123.75)/(24.75) \\ \\ x=5 \end{gathered}`

Then, there are 5 adults (x=5) and 3 children (y=3) in Gonzalez family