At Systemopia adventure park you must buy a ticket to go on each ride. The three

Question

At Systemopia adventure park you must buy a ticket to go on each ride. The three types of rides at Systemopia are classified as either fun, fantastic, or fabulous and each type of ride costs a different amount. The cost of two fun rides and four fantastic rides is $22.34. The cost of eight fantastic rides and five fabulous rides is $96.21. The cost of seven fabulous rides and ten fun rides is $88.21. How much money will it cost to go on one fun ride, nine fantastic rides, and six fabulous rides? Express your answer to the nearest cent and show all work

Explanation / Answer

Let a = fun ticket; b = fantastic; c = fabulous 2a + 4b = 22.34 8b + 5c = 96.21 7c + 10a = 88.21 This is a system of three equations with three unknowns. Idon't know how your teacher expects you to solve this (there areseveral methods to choose from). This is one way: Rewrite the equations: 2a + 4b + 0c = 22.34                                   0a + 8b + 5c = 96.21                                   10a+ 0b + 7c = 88.21 Multiply the first equation by -2, then add the first andsecond equations: (-4a -8b + 0c = -44.68) + (0a + 8b + 5c = 96.21) This eliminates the b term: -4a  + 5c = 51.53 Multiply the new equation by 5 and the third equation by 2,then add these two equations: (-20a +25c = 257.65) + (20a + 0b + 14c = 176.42) This eliminates the a: 39c = 434.07, so c = 11.13. Now, substitute this value into the second equation to find b.Substitute that value into the first equation to find a.

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