A certain zoo sold admissions tickets to groups of 20 people every 10

Question

A certain zoo sold admissions tickets to groups of 20 people every 10 minutes from 5:00 p.m. until 9:00 p.m., inclusive. Tickets for children cost $7 each, and tickets for adults cost $22 each. If the zoo's ticket revenue on a certain day was $5000, how many adult tickets were sold?

(A) 80

(B) 100

(C) 110

(D) 128

(E) 150

(A) 80

(B) 100

(C) 110

(D) 128

(E) 150

Bunuel · Accepted Answer

GMATNinja Video Solution:

https://www.youtube.com/watch?v=RAVTJPmkGSA

Reon · Answer

5 pm to 9 pm = 4 hours and it is given inclusive so we will also include endpoint.
Admission tickets are sold to 20 people every 10 mins. In 1 hr, it would be 120 people and in 4 hours, it would be 120*4=480 people and since timing is inclusive, Total = 480+20=500.

C+A= 500 or C= 500-A
Also, 7C+22A= 5000 
7(500-A)+22A =5000
3500 -7A +22A =5000
15A=5000-3500=1,500 
A=1500/15=100

B) 100

agil31 · Answer

The total hours seem to be coming upto only 480 hours. Number of adults after solving the equations is 109. Closest option is 110, but it is wrong. Please help

egmat · Answer

Hi agil31,

Your equations are set up perfectly; the only slip is in the head-count. You landed on  480  people, and once that feeds into the equation you get a =  109.33 , which rounds toward  110  - but the real total is  500 , and that's what gives the clean answer of  100 .

Look again at Reon's solution: after getting  480 , they added a  +20 . That extra group is the whole game, so let me show why it belongs.

Why it's 25 groups, not 24

The zoo sells a group  at every 10-minute mark  from  5:00  to  9:00 , and "inclusive" means both  5:00  and  9:00  count. So the sale times are:

5:00, 5:10, 5:20, ... , 8:50,  9:00

That's  4  hours =  240  minutes. Dividing by  10  gives  24  - but that  24  counts the  gaps between  marks, not the marks themselves. Whenever you count fence posts, the number of posts is one more than the number of gaps:

- Gaps:  240  /  10  =  24 
- Marks (groups):  24  +  1  =  25

So total people =  25  x  20  =  500 , which is Reon's  480  + the one endpoint group of  20 .

Plug  500  in and it falls out cleanly: 7(500 - a) + 22a = 5000 -> 3500 + 15a = 5000 -> a =  100 .

Quick check to lock the habit

How many  10 -minute marks are there from  1:00  to  1:30  inclusive? Gaps:  30 / 10  =  3 . Marks: 1:00, 1:10, 1:20, 1:30 =  4 . Always one more than the gap count.

Whenever a problem says "inclusive," pause and add that final post - it's exactly the  20  you were missing.

Answer: B

A certain zoo sold admissions tickets to groups of 20 people every 10

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A certain zoo sold admissions tickets to groups of 20 people every 10

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