describe this math problem?

Question

Darren is seeling tickets for the school play. Regular tickets are $4.00 each and student tickets are $3.00 eac. Darren sells a total of 190 tickets and collects $650. How many of each kind of ticket did he sell?



Im NOT looking of the answer, DONT solve it.



My question is, how would you descride this problem and what type of problem is it? What type of math concept is being addressed? Also, what makes it easy or difficult or easy to solve.



Thank you!

Answer 1

let

x = student tickets

y = regular tickets

190 = total tickets

3x = cost of students

4x = cost of regular tickets

650 = total amount collected

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x + y = 190- - - - - - -Equation 1
3x + 4y = 650- - - - -Equation 2
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Substitute method equation 1

x + y = 190

x + y - x = - x + 190

y = - x + 190

substiture the y value into equation 2
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3x + 4y = 650

3x+ 4(- x + 190) = 650

3x + ( - 4x + 760) = 650

3x - 4x + 760 = 650

- x + 760 - 760 = 650 - 760

- x = - 110

-1(- x) = - 1(- 110)

- (- x) = - (- 110)

x = 110

Insert the x value into equation 1

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x + y = 190

110 + y = 190

110 + y - 110 = 190 - 110

y = 80

Insert the y value into equation 1

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Check for equation 1

x + y = 190

110 + 80 = 110

110 = 110

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Check for equation 2

3x + 4y = 650

3(110) + 4(80) = 650

330 + 320 = 650

650 = 650

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Both equations balance

The solution set is { 110, 80 }

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Answer 2

This can be solved using a simple system of simultaneous equations,geometrically the solution represents the point of intersection of two straight lines.However note that these are actually trivial cases of linear programming problems in operations research.

Answer 3

This is algebra.

Put x for number of regular tickets and y for student tickets.

so you have two equations:
For total revenue: 4x + 3y = 650
For total tickets: x + y = 190

Solving them will give your answer.

Answer 4

its simultaneous equations
4r + 3s = 650
r + s = 190

its fairly easy because the numbers / coeffs are easy