alphak3nny001 wrote:
A museum sold 30 tickets on Saturday. Some of the tickets sold were $10 general exhibit tickets and the rest were $70
special exhibit tickets. How many general exhibit tickets did the museum sell on Saturday?
(1) The museum's total revenue from ticket sales on Saturday was greater than $1,570 and less than $1,670.
(2) The museum sold more than 20, but fewer than 25, special exhibit tickets on Saturday.
\(\left. \begin{gathered}
\$ 10/\,{\text{each}}\,\,G\,\,\, \hfill \\
\$ 70/\,{\text{each}}\,\,S \hfill \\
\end{gathered} \right\}\,\,\,\,\,G + S = 30\,\,\,\left( * \right)\,\,\,\,\,\,\,\,\,\,\,\,;\,\,\,\,\,\,\,\,\,\,? = G\)
\(\left( 1 \right)\,\,\,1570 < 10G + 70S < 1670\)
\(10G + 70S\,\,\,\mathop = \limits^{\left( * \right)} \,\,\,10G + 70\left( {30 - G} \right) = 60\left( {35 - G} \right)\,\,\, \Rightarrow \,\,\,{\text{multiple}}\,\,{\text{of}}\,\,60\)
\(\frac{1570}{60} = \frac{1200 + 360 + 10}{60} = 26\frac{1}{6}\)
\(\frac{1670}{60} = \frac{1200 + 420 + 50}{60} = 27\frac{5}{6}\)
\(\Rightarrow \,\,\,\,60\left( {35 - G} \right) = 27 \cdot 60\,\,\,\,\,\,\, \Rightarrow \,\,\,\,G\,\,{\text{unique}}\)
\(\left( 2 \right)\,\,\,20 < S < 25\,\,\,\,\,\,\mathop \Leftrightarrow \limits^{\left( * \right)} \,\,\,\,\,\,\,20 < 30 - G < 25\,\,\,\,\, \Leftrightarrow \,\,\,5 < G < 10\,\,\,\)
\(\left\{ \begin{gathered}
G = 6\,\,\,\,\,\left( {S = 24} \right)\,\,\,\,\,\,{\text{viable}} \hfill \\
G = 7\,\,\,\,\,\left( {S = 23} \right)\,\,\,\,\,\,{\text{viable}} \hfill \\
\end{gathered} \right.\,\)
This solution follows the notations and rationale taught in the GMATH method.
Regards,
fskilnik.
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