Marion L. answered • 02/16/15
Tutor
4.9
(1,228)
TEST PREP and ACADEMIC SUBJECTS
Hi Shelby,
This is obviously a multi-step problem.
STEP ONE: The first thing you have to deal with is how to allocate the 400 tickets to the various price groups.
You know that
Group (A), the ($8 ,$10) tickets sold = 7 times
Group (B), the $12 tickets sold = 1 time
This means for every 1 ticket you sold out of the $12 group, you sold 7 tickets (7x1) out of the ($8 ,$10) group. So, the total number of tickets must be divisible by 8 (seven plus one) which 400 definitely is, because 400/8=50.
Now just multiply
7x50=350 tickets sold from the ($8,$10) group and
1x50=50 tickets sold from the $12 group
STEP TWO: Assess what you know .
Now we know some more information. We know that there were 50 tickets sold from the $12 group, so a total of $600 was raised from the sale of the $12 tickets ($12x50).
We also know that the total sales for all tickets were $3700. So that must mean that the ($8, $10) ticket group brought in $3100.
STEP THREE: The next challenge is to allocate the $3100 to the $8 tickets and to the $10 tickets. At this point you can either play around with the numbers a little to see if you can get the answer, keeping in mind that the total number of combined $8 and $10 tickets sold has to be 350 and the total has to be $3100.
Doing this algebraically,
8 [350-n] + 10 [350- (350-n)]= 3100
Solve for n=150
Plug 150 back into the equation to get 8 [200] + 10 [150]=3100
Now you know that 200 of the $8 tickets were sold for a total of $1600, and 150 of the $10 tickets were sold for a total of $1500.
To Summarize:
$8 tickets: 200 sold ($1600)
$10 tickets: 150 sold ($1500)
$12 tickets: 50 sold ($600)
