Question

A family of 2 children and 1 adult visited an amusement park and paid an entry fee of $90. Another family of 3 children and 2 adults visited the same amusement park and paid an entry fee of $155. What is the entry fee for a child at the amusement park?

Answer 1

`\underline{\underline{\large\bf{Solution:-}}}\\`

`\leadsto`Let us assume entry fee for child be x

`\leadsto`Let us assume entry fee for adult be y

`\\`

`\longrightarrow`Since Entry fees for 2 children and 1 adult is $90 an equation for entry fees will be formed as -

`\begin{gathered}\\\implies\quad \sf 2* x + 1 * y = 90 \\\end{gathered}`

`\begin{gathered}\\\implies\quad \sf 2 x + y = 90 \\\end{gathered} \_\_\_\_\_(1)`

`\longrightarrow`Similarly, Entry fees for 3 children and 2 adult is $155 , so an equation for entry fees will be formed as -

`\begin{gathered}\\\implies\quad \sf 3* x + 2* y = 155 \\\end{gathered}`

`\begin{gathered}\\\implies\quad \sf 3x + 2y = 155 \\\end{gathered} \_\_\_\_\_(2)`

Multiplying eq (1) by 2 it will be -

`\begin{gathered}\\\implies\quad \sf 4x + 2y = 180\\\end{gathered}\_\_\_\_\_(3)`

Subtracting eq(2) from eq(3) -

`\begin{gathered}\\\implies\quad \sf 4x+2y - (3x+2y) = 180-155\\\end{gathered}`

`\begin{gathered}\\\implies\quad \sf 4x + 2y - 3x - 2y = 35\\\end{gathered}`

`\begin{gathered}\\\implies\quad \sf 4x - 3x +2y- 2y = 35\\\end{gathered}`

`\begin{gathered}\\\implies\quad \bf x = 35\\\end{gathered}`

Thus , entry fee for a child at the amusement park = $ 35