A museum sold 30 tickets on Saturday. Some of the tickets

i did following:
General=G Special=S
G+S =30
70*S+ 30*G= Revenue

Statement 1:
1570<Revenue<1670

70*S+70*G=2100
70*S+ 30*G= 1660 [Within the range]

40G=440
G=11

70*S+70*G=2100
70*S+ 30*G= 1620 [Within the range]

40G= 480
G=12

I am having multiple integer value for General tickets G[11, 12]. What am i doing wrong?

Revenue=70S+10G not 70S+30G.

Excellent Question..
Does anyone have a list of such questions?
Word problems based on inequality..

Posting official solution of this problem.

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.

Merging topics. Please search before posting.

tickets: a+b=30
sales: 10a+70b

(1) The museum’s total revenue from ticket sales on Saturday was greater than $1,570 and less than $1670: sufic.

\(1570<10a+70b<1670…1570<10(30-b)+70b<1670…1570<300+60b<1670…\)
\(1270<60b<1370…127/6<b<137/6…21.15<b< 22.8…21<b<23…b=22…a=8\)

(2) The museum sold more than 20, but fewer than 25, special exhibit ticket on Saturday: insufic.

\(20<b<25…b=[21,22,23,24]\)

Answer (A)

general exhibit tickets = $10
special exhibit tickets = $70

g + s = 30

let g: number of general exhibit tickets sold
let 30-g: special exhibit tickets sold

(1) The museum’s total revenue from ticket sales on Saturday was greater than $1,570 and less than $1670.

1570 < 10(g) + 70(30-g) < 1670
1570 < 10g + 210-70g < 1670
-530 < -60g < -430
430 < 60g < 530
7 < g < 9
g = 8. SUFFICIENT

(2) The museum sold more than 20, but fewer than 25, special exhibit ticket on Saturday.

Clearly insufficient -- we don't know the total revenue.

Answer is A.

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