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Diano4ka-milaya [45]
2 years ago
8

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 ad

ults visited the same amusement park and paid an entry fee of $155. What is the entry fee for a child at the amusement park?
Mathematics
1 answer:
stiks02 [169]2 years ago
7 0

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

\leadstoLet us assume entry fee for child be x

\leadstoLet us assume entry fee for adult be y

\\

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

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

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

\longrightarrow<u>Similarly, Entry fees for 3 children and 2 adult is </u><u>$</u><u>1</u><u>5</u><u>5</u><u> , so an equation for entry fees will be formed as -</u>

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

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

<u>Multiplying eq (1) by </u><u>2</u><u> </u><u>it will be - </u>

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

<u>Subtracting</u><u> eq(</u><u>2</u><u>) </u><u>from</u><u> eq(</u><u>3</u><u>) - </u>

\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

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