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

Question

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 $1670.
(2) The museum sold more than 20, but fewer than 25, special exhibit ticket on Saturday.

Bunuel · Accepted Answer

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?

Say the museum sold $G$ general exhibit tickets and $30-G$ special exhibit tickets, then the museum's total revenue wold be $10G+70(30-G)=2100-60G$.

(1) The museum’s total revenue from ticket sales on Saturday was greater than $1,570 and less than $1670 --> $1570<2100-60G<1670$ --> $-530<-60G<-430$ --> reduce by -10 and flip the sign: $43<6G<53$ --> since $G$ must be an integer then $G=8$. Sufficient.

(2) The museum sold more than 20, but fewer than 25, special exhibit ticket on Saturday --> $20<S<25$ --> $S$ could be be 21, 22, 23 or 24, so $G$ could be 9, 8, 7, or 6 respectively. Not sufficient.

Answer: A.

Hope it's clear.

cyberjadugar · Answer

Hi,

let there be x tickets sold at $10,
so, the tickets sold at $70 would be (30-x).
and total revenue would be: $10(x)+$70(30-x)

Using (1)
1570 < 10(x)+70(30-x) < 1670
or 1570 < 10x + 2100 - 70x < 1670
or 1570-2100 < -60x < 1670-2100
or -530 < -60x < -430 (multiply by -1)
or 430 < 60x < 530
or 7.16 < x < 8.33,
since x is integer and only one value exist between 7.1 & 8.3, i.e., 8
thus, x=8. Sufficient.

Using (2),
20 < special exhibit ticket < 25
or 20 < 30-x < 25
or -10 < -x < 5
or 5 < x <10,
thus, x = 6, 7, 8, 9
Clearly, not sufficient.

Thus, Answer is (A).

Regards,

BDSunDevil · Answer

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

40G=440
G=11

70*S+70*G=2100
70*S+ 30*G= 1620

40G= 480
G=12

I am having multiple integer value for General tickets G . What am i doing wrong?

Bunuel · Answer

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

stonecold · Answer

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

anairamitch1804 · Answer

Posting official solution of this problem.

alphak3nny001 · Answer

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.

fskilnik · Answer

\left. \begin{gathered}
 \$ 10/\,{	ext{each}}\,\,G\,\,\, \hfill \
 \$ 70/\,{	ext{each}}\,\,S \hfill \ 
\end{gathered} ight\}\,\,\,\,\,G + S = 30\,\,\,\left( * ight)\,\,\,\,\,\,\,\,\,\,\,\,;\,\,\,\,\,\,\,\,\,\,? = G

\left( 1 ight)\,\,\,1570 < 10G + 70S < 1670

10G + 70S\,\,\,\mathop = \limits^{\left( * ight)} \,\,\,10G + 70\left( {30 - G} ight) = 60\left( {35 - G} ight)\,\,\, \Rightarrow \,\,\,{	ext{multiple}}\,\,{	ext{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} ight) = 27 \cdot 60\,\,\,\,\,\,\, \Rightarrow \,\,\,\,G\,\,{	ext{unique}}

\left( 2 ight)\,\,\,20 < S < 25\,\,\,\,\,\,\mathop \Leftrightarrow \limits^{\left( * ight)} \,\,\,\,\,\,\,20 < 30 - G < 25\,\,\,\,\, \Leftrightarrow \,\,\,5 < G < 10\,\,\,

\left\{ \begin{gathered}
 G = 6\,\,\,\,\,\left( {S = 24} ight)\,\,\,\,\,\,{	ext{viable}} \hfill \
 G = 7\,\,\,\,\,\left( {S = 23} ight)\,\,\,\,\,\,{	ext{viable}} \hfill \ 
\end{gathered} ight.\,

This solution follows the notations and rationale taught in the GMATH method.

Regards,
fskilnik.

Bunuel · Answer

Merging topics. Please search before posting.

exc4libur · Answer

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=

Answer (A)

Basshead · Answer

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.

bumpbot · Answer

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

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