Question

The school field trip for December is to the local Holiday Festival where there are horse drawn carriage and sleigh rides. Every student gets to take the horse drawn carriage or the sleigh ride. In the first hour 4 horse drawn carriage rides and 5 sleigh rides took a total of 132 students. In the second hour 6 horse drawn carriage rides and 4 sleigh rides took a total of 156 students. If the same number of students rode on each horse drawn carriage ride and the same number of students rode on each sleigh ride, how many students rode on each horse drawn carriage ride? How many students rode on each sleigh ride?

Answer 1

Let us formulate a system of equations to solve this problem.

Let x represent the number of students rode on each horse drawn carriage.

Let y represent the number of students rode on each sleigh ride.

4x + 5y = 132 Equation 1

6x + 4y = 156 Equation 2

We are going to use the elimination method to solve the system.

12x + 15y = 396 (Multiplying the first equation by 3)

12x + 8y = 312 (Multiplying the second equation by 2)

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7y = 84 ( Subtracting last form of equation 2 from last form of equation 1)

y=12 (Dividing on both sides of the equation by 7)

Replacing y=12 in the original form of Equation 1

4x + 5(12) = 132

4x + 60 = 132 (Multiplying)

4x = 72 (Subtracting 60 from both sides of the equation)

x= 18 (Dividing on both sides of the equation by 4)

The answer is 18 students rode on each horse drawn carriage and 12 students rode on each sleigh ride.