Respuesta :
[tex]\underline{\underline{\large\bf{Solution:-}}}\\[/tex]
[tex]\leadsto[/tex]Let us assume entry fee for child be x
[tex]\leadsto[/tex]Let us assume entry fee for adult be y
[tex]\\[/tex]
[tex]\longrightarrow[/tex]Since Entry fees for 2 children and 1 adult is $90 an equation for entry fees will be formed as -
[tex]\begin{gathered}\\\implies\quad \sf 2\times x + 1 \times y = 90 \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf 2 x + y = 90 \\\end{gathered} \_\_\_\_\_(1) [/tex]
[tex]\longrightarrow[/tex]Similarly, Entry fees for 3 children and 2 adult is $155 , so an equation for entry fees will be formed as -
[tex]\begin{gathered}\\\implies\quad \sf 3\times x + 2\times y = 155 \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf 3x + 2y = 155 \\\end{gathered} \_\_\_\_\_(2) [/tex]
Multiplying eq (1) by 2 it will be -
[tex]\begin{gathered}\\\implies\quad \sf 4x + 2y = 180\\\end{gathered}\_\_\_\_\_(3) [/tex]
Subtracting eq(2) from eq(3) -
[tex]\begin{gathered}\\\implies\quad \sf 4x+2y - (3x+2y) = 180-155\\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf 4x + 2y - 3x - 2y = 35\\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf 4x - 3x +2y- 2y = 35\\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \bf x = 35\\\end{gathered} [/tex]
Thus , entry fee for a child at the amusement park = $ 35
