At an amusement park, the cost of 3 adult tickets and 4 children's tickets is $126.50. Another customer paid $120.50 for 2 adult tickets and 5 children's tickets. What is the price of each kind of ticket?

the cost of an adult ticket is $21.5

the cost of a child ticket is $15.5

Step-by-step explanation:

Let x represent the cost of an adult ticket.

Let y represent the cost of a child ticket.

At an amusement park, the cost of 3 adult tickets and 4 children's tickets is $126.50. It means that

3x + 4y = 126.5- - - - - - - - - - - -1

Another customer paid $120.50 for 2 adult tickets and 5 children's tickets. It means that

2x + 5y = 120.5- - - - - - - - - - - -2

Multiplying equation 1 by 2 and equation 2 by 3, it becomes

6x + 8y = 253

6x + 15y = 361.5

Subtracting, it becomes

- 7y = - 108.5

y = - 108.5/ - 7

y = 15.5

Substituting y = 15.5 into equation 1, it becomes

3x + 4 × 15.5 = 126.5

3x + 62 = 126.5

3x = 126.5 - 62

3x = 64.5

x = 64.5/3

x = 21.5

the quotient is 4x^2 - 27x + 167 with a remainder of -996

step-by-step explanation:

in synthetic division, use -6 as the divisor and use the coefficients {4, -3, 5, 6}:

-6     )   4     -3     5     6

                -24   162 -1002

          4   -27   167   -996

thus, the quotient is 4x^2 - 27x + 167 with a remainder of -996.

note:   your "4x°-3x+5x+6" is ambiguous / incomplete.   i had to assume that you meant '4x^3 - 3x^2 + 5x + 6."

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step-by-step explanation: