AMC12 2014 A

AMC12 2014 A · Q2

AMC12 2014 A · Q2. It mainly tests Linear equations, Fractions.

At the theater children get in for half price. The price for $5$ adult tickets and $4$ child tickets is $\$24.50$. How much would $8$ adult tickets and $6$ child tickets cost?

剧院儿童票半价。5张成人票和4张儿童票的价格是$24.50$。8张成人票和6张儿童票需要多少钱？

(A) \$35 \$35

(B) \$38.50 \$38.50

(D) \$42 \$42

(E) \$42.50 \$42.50

Answer

Correct choice: (B)

正确答案：（B）

Solution

Suppose $x$ is the price of an adult ticket. The price of a child ticket would be $\frac{x}{2}$. \begin{eqnarray*} 5x + 4(x/2) = 7x &=& 24.50\\ x &=& 3.50\\ \end{eqnarray*} Plug in for 8 adult tickets and 6 child tickets. \begin{eqnarray*} 8x + 6(x/2) &=& 8(3.50) + 3(3.50)\\ &=&\boxed{\textbf{(B)}\ \ 38.50}\\ \end{eqnarray*}

设$x$为成人票价格，则儿童票价格为$\frac{x}{2}$。 \begin{eqnarray*} 5x + 4(x/2) = 7x &=& 24.50\\ x &=& 3.50\\ \end{eqnarray*} 代入8张成人票和6张儿童票： \begin{eqnarray*} 8x + 6(x/2) &=& 8(3.50) + 3(3.50)\\ &=&\boxed{\textbf{(B)}\ \ 38.50}\\ \end{eqnarray*}

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