Question

13a) mrs. evans is taking 9 students to an amusement park. mr. sanchez is taking 14 students to a water park. each student will buy a ticket to the appropriate park and pay for a ride fee. admission to the amusement park is 2 times that of the water park’s admission as shown in the table. the total cost is the same for both groups of students.

amusement park	water park
ride fee: $3.00	ride fee: $4.50

which equation represents the problem?
○ a) $9(x + 4.50) = 14(2x + 3.00)$
○ b) $9(x + 3.00) = 14(2x + 4.50)$
○ c) $9(2x + 4.50) = 14(x + 3.00)$
○ d) $9(2x + 3.00) = 14(x + 4.50)$
13b) mrs. evans is taking 9 students to an amusement park. mr. sanchez is taking 14 students to a water park. each student will buy a ticket to the appropriate park and pay for a ride fee. admission to the amusement park is 2 times that of the water park’s admission as shown in the table. the total cost is the same for both groups of students.

amusement park	water park
ride fee: $3.00	ride fee: $4.50

what is the admission price per student to the amusement park?
$___

1. place an x in the appropriate cell to indicate whether each equation has one solution, no solution or infinitely many solutions.

	one solution	no solutions	infinitely many solutions
$3(4x - 4) = 4(3x - 3)$
$4(x - 5) = 2(9 + 2x)$

Explanation:

13A)

Step1: Analyze Amusement Park Cost

For Mrs. Evans' group (9 students at amusement park), each student's cost is admission (\(2x\)) plus ride fee (\(3.00\)), so total cost is \(9(2x + 3.00)\).

Step2: Analyze Water Park Cost

For Mr. Sanchez' group (14 students at water park), each student's cost is admission (\(x\)) plus ride fee (\(4.50\)), so total cost is \(14(x + 4.50)\).

Step3: Set Costs Equal

Since total costs are equal, the equation is \(9(2x + 3.00)=14(x + 4.50)\), which matches option D.

Step1: Use the Equation from 13A

We have the equation \(9(2x + 3.00)=14(x + 4.50)\).

Step2: Expand Both Sides

Left: \(9\times2x + 9\times3.00 = 18x + 27\)
Right: \(14\times x + 14\times4.50 = 14x + 63\)

Step3: Solve for \(x\)

Subtract \(14x\) from both sides: \(18x - 14x + 27 = 63\)
Simplify: \(4x + 27 = 63\)
Subtract 27: \(4x = 63 - 27 = 36\)
Divide by 4: \(x = \frac{36}{4} = 9\)

Step4: Find Amusement Park Admission

Amusement park admission is \(2x\), so \(2\times9 = 18\).

Step1: Expand Both Sides

Left: \(10x + 6\)
Right: \(6x + 48 + 2 = 6x + 50\)

Step2: Solve for \(x\)

Subtract \(6x\) and 6: \(10x - 6x = 50 - 6\)
\(4x = 44\)
\(x = 11\) (one solution)

Equation 2: \(3(4x - 4)=4(3x - 3)\)

Answer:

D) \(9(2x + 3.00) = 14(x + 4.50)\)

13B)