SOLUTION: Ticket sales: A science museum charges $10 for a regular admission ticket, but members recieve a discount of $3 and students are admitted for $5. Last saturday, 750 tickets were so

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Question 164624This question is from textbook
: Ticket sales: A science museum charges $10 for a regular admission ticket, but members recieve a discount of $3 and students are admitted for $5. Last saturday, 750 tickets were sold for a total of $5400. If 20 more student tickets than regular tickets were sold, how many of each type of ticket were sold?
I need to know the steps in which they used to solve this? This question is from textbook

Answer by MRperkins(300) (Show Source):
You can put this solution on YOUR website!
Ok, the first thing we need to do is set up our formulas.
Let's use:
r = regular admission tickets = $10
m = members admission tickets = $7
s = student admission tickets = $5
So we know that 750 tickets were sold so:

and
We know the price of the tickets and the total dollar amount sold was $5400 so:
Price of each ticket times the number of that ticket sold equals $5400 or:

We also know that 20 more student tickets than regular tickets were sold so:

Now for the fun part :/)
Use the elimination method to solve:
10r+7m+5s=5400
r+ m+ s=750
We want to eliminate m because it is the only variable that is not in the s=r+20 equation.
so:
Multiply everything in the bottom equation by 7.
10r+ 7m+ 5s=5400
(7)r+(7)m+(7)s=(7)750
OR
10r+7m+5s=5400
7r+7m+7s=5250
Now we can subtract and get

combine like terms:

Now it is time to use the equation:
Substitute r+20 for s so:

Distribute

combine like terms

add 40 to both sides and get
now substitute 190 for r in the equation and solve for s:
and you get
go back to the first equation and plug in 190 for r and 210 for s:

Solve for m:
combine like terms:

subtract 400 from both sides:

Elimination and substitution are fun. It gets better as you get used to them.