Question

Could someone help me set this problem up....

Answer 1

At a concert, tickets were sold at $12,$30 and $50. The sales of $12 tickets made up 25% of the total amount of money collected. The sales of $30 made up 60% of the total amount. Given that 5 more $12 tickets were sold then $30 tickets,how many $50 tickets were sold ?

I already know that $50 tickets made up 15% of the total amount. I am just having trouble setting the problem up.

Answer 2

@whpalmer4 .....can you help me

Answer 3

@Mertsj ...can you help me

Answer 4

I know this is probably gonna be easy.....my mind just isn't catching on very fast tonight :/

Answer 5

@genius12 ...can you help

Answer 6

This is not multiple choice...if it was I could easily figure out the answer

Answer 7

I started thinking like this.....x = $12, y = $30, z = $50.
12x + 30y + 50z = the total
and 5 more $ 12 tickets were sold then $30 tickets : y + 5 = x.
And then I got lost again.

Answer 8

@ganshie....help please

Answer 9

@ganeshie8

Answer 10

\[\bf 0.25x=12y\]\[\bf 0.6x=30z\]\[\bf 0.15x=50(z+5)\]So solve for 'x' and 'z' from the bottom two equations and then plug that value of 'x' in to the first equation and solve for 'y'. Get it?

@texaschic101

Answer 11

.6x = 30z
x = 30/.6z
x = 50z

am I doing this right ?

.15x = 50(z + 5)
.15(50z) = 50z + 250
7.5z = 50z + 250
I am not doing this right am I ....this is gonna end up negative

Answer 12

I dont understand where you are getting some of these numbers

Answer 13

\[12x+30y+50z = N\]
\[y = x-5\]
\[0.25N = 12x\]
\[0.6N = 30y = 30(x-5)\]
you can solve a system of 2 equations for x and N

Answer 14

You've got X of total revenue
0.25 X = 12A
0.6 X = 30B
0.15 X = 50 C
A-5 = B

0.25 X = 12A
X = 48A

0.6(48A) = 30B

make our system of equations:

0.6(48A) - 30B = 0
A - B = 5
B = A-5

0.6(48A) - 30(A-5) = 0

-1.2A +150 = 0
A = 125
125 $12 tickets sold
B = A - 5 = 125 - 5
120 $30 tickets sold
total revenue was 48A = 48*125 = 6000
C ticket revenue was 0.15 * 6000 = 50 C
C = 18
18 $50 tickets sold

checking:

25% of 6000 = 1500 or 125@$12
60% of 6000 = 3600 or 120@$30
15% of 6000 = 900 or 18@$50

Answer 15

wow...your good

Answer 16

does that all make sense to you? I didn't format it as neatly as I often do...

Answer 17

This problem was a little more complicated then I thought......I figured it was easy and I didn't see it.....again, wow your good

Answer 18

I can see what you did.....I am understanding it. I was way off. Thank you so much.......thanks for everybody's help

Answer 19

it's sort of like the time/distance problems where you don't actually know the distance, but it turns out not to matter...

Answer 20

I know right......thanks again :)

Answer 21

you're welcome! thanks for the interesting problem :-)

Answer 22

The problem easy with an easy approach. Sorry I was afk, did you solve the equations I gave you? @texaschic101

Answer 23

yes....it took me awhile....but thank you

Answer 24

I love OS

Answer 25

I will close this now.....thanks everyone

Answer 26

btw, @genius12 the equations you gave weren't quite right.

0.25x = 12y
0.6x = 30(y-5)
0.15x = 50z

gives solutions of x = 6000, y=125, z = 18

Answer 27

@whpalmer4 Oh I accidentally wrote 5 more $50 tickets instead of 5 more $12 tickets than $30 tickets. Probably misread something. Ty for pointing that out.

Answer 28

easy to do! that's why I always take a fresh look at the problem statement as I check my answers...

Answer 29

After fixing:\[\bf 0.25x=12(y+5)\]\[\bf 0.6x=30y\]\[\bf 0.15x=50z\]Now I get the same solution as you.

@whpalmer4

Answer 30

Yep, that's correct! The solutions from the other set were uh, more interesting :-)

x = -294.118, y = -6.12745, z = -5.88235