Pls assist..
1) 3 persons, X, Y & Z were to paint a wall. If the job were to be done by one person, X, Y & Z would take 6 hrs, 8hrs & 12 hrs respectively to complete. X & Y painted for 3 hrs after which X rested. Y & Z then continued with the painting. How many hours would it take for the wall to be painted? (answer in mixed number.)
2) A drama company sold some tickets for a performance. It sold the same number of $8 & $5 tickets on the first day and collected $1664. It then sold 96 $8 tickets than $5 tickets on the next day. If it collected $632 more from the sale of $8 tickets than the $5 tickets from the two days, how many $8 tickets were sold in total?
tks & rgds.
X : Y : Z
6 : 8 : 12
every 1 hour X paints 1/6 of the wall
every 1 hour Y paints 1/8 of the wall
every 1 hour Z paints 1/12 of the wall
3 hours -- X paints 1/6 x 3 = 1/2
3 hours -- Y paints 1/8 x 3 = 3/8
together, they painted 7/8 of the wall
Y + Z paint remaining 1/8 of the wall
1/8 + 1/12 = 5/24
1/8 / 5/24 = 3/5h
3 + 3/5 = 3.3/5h
2) A drama company sold some tickets for a performance. It sold the same number of $8 & $5 tickets on the first day and collected $1664. It then sold 96 (is there a "more" missing here?) $8 tickets than (or is this "and" and not "than"?) $5 tickets on the next day. If it collected $632 more from the sale of $8 tickets than the $5 tickets from the two days, how many $8 tickets were sold in total?
apologies,re-wrote the question below:
A drama company sold some tickets for a performance. It sold the same number of $8 & $5 tickets on the first day and collected $1664. It then sold 96 $8 tickets and $5 tickets on the next day. If it collected $632 more from the sale of $8 tickets than the $5 tickets from the two days, how many $8 tickets were sold in total?
On the first day,
number of $8 tickets sold = number of $5 tickets sold = $1664 / ($8 + $5) = 128.
therefore on the first day alone, they collected 128 x ($8 - $5) = $384 more from the $8 tickets.
meaning on the second day, they collected $248 more from the $8 tickets.
(from here on in i'm trying my best not to use algebra, any alternative method??)
If they had sold equal number of $8 and $5 on the second day (48 tickets each), the amount collected more from $8 ticket willbe $48 x 3 = $144.
For every 1 $5 ticket they sell less and 1 $8 ticket more, they will collect $13 more.
$248 = $144 + $13 x 8
Means that they sold 48 - 8 = 40 $5 tickets and 48+8 = 56 $8 tickets on the second day.
Therefore they sold 128 + 56 = 184 $8 tickets.