Help with math

Question

Ninety-six passengers rode in a train from city a to city b. Tickets for regular coach seats cost $124. Tickets for sleeper cars seats cost $288. The receipts for the trip totaled $20,760. How many passengers purchased each type of ticket?  The number of coach tickets purchased was? The number of sleeper car tickets purchased was?

Answer 1

Here we need to solve a system of equations. Let the people in coach be represented by an X and the people in the sleeper cars be represented by a Y

 

To solve this problem, we need to set up the information given in the question:

 

124X + 288Y = 20760

 

SUCH THAT

 

X + Y = 96

 

we can now rearrange the constraint equation to solve for the original equation. let X + Y = 96 --> Y = 96 - X, Therefore:

124X + 288Y = 20760 => 124X + 288(96-x) = 20760 --> 124X + 27548 - 96X = 20760,

 

We can now solve the problem by combining like terms. We get that X = 42, therefore when we plug X back into the constraint equation we get 96 - 42 = Y --> Y = 54