SOLUTION: I hope I put it under the correct topic. I need some help in working out the steps to solve this problem, mainly to help me learn how to identify and set the variables to solve th

Question 216524: I hope I put it under the correct topic. I need some help in working out the steps to solve this problem, mainly to help me learn how to identify and set the variables to solve the equation. (Please remember I am taking very basic algebra of graphs and functions.) Thank you in advance!
Please help me solve the following:
One evening 750 tickets were sold for Shortridge Community College's spring musical. Tickets cost $3.00 for students and $5.00 for non-students. Total receipts were $3066. How many of each type of ticket were sold?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
One evening 750 tickets were sold for Shortridge Community College's spring musical.
Tickets cost $3.00 for students and $5.00 for non-students.
Total receipts were $3066. How many of each type of ticket were sold?
:
Let x = no. of student tickets
Let y = no. of non-student tickets
:
Total tickets sold equation
x + y = 750
:
Total $receipts equation
3x + 5y = 3066
:
We can rearrange the 1st equation in a form to use for substitution in the 2nd equation:
x + y = 750
subtract y from both sides, and we have:
x = 750 - y
:
Substitute (750-y) for x in the 2nd equation
3x + 5y = 3066
3(750-y) + 5y = 3066
Multiply what's inside the brackets
2250 - 3y + 5y = 3066
Subtract 2250 from both sides and you have
-3y + 5y = 3066 - 2250
2y = 816
divide both sides by 2
y =
y = 408 non-student tickets
then we know
x = 750 - y
x = 750 - 408
x = 342 student tickets
:
:
Check solutions in original receipt equation
3(342) + 5(408) =
1026 + 2040 = 3066; confirms our solutions
;
Was this basic enough? ankor@att.net

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