Question

use the following information to answer the next question.
a school is selling tickets to a concert. a student creates a system of equations to model ticket sales.
they use the variable x to represent the number of adult tickets which cost $7 each. the variable y represents the number of student tickets which cost $5 each.

1. which is a possible solution to their system?

a. \t\tx = 57
\t\ty = 43
b. \t\tx = -57
\t\ty = 43
c. \t\tx = 56.8
\t\ty = 43.1
d. \t\tx = 56.8
\t\ty = -43.1

use the following information to answer the next question.
a group of grade 10 and 11 students are going on a field trip. the school has booked both vans and buses to transport the students.
there are 6 vans and 1 bus booked to transport the 68 grade 11 students.
there are 4 vans and 3 buses booked to transport the 120 grade 10 students.

1. assuming that each van and each bus is transporting the same number of students, create a system that could be used to determine how many students each mode of transportation can carry.

a. \t\t6x + y = 68
\t\t4x + 3y = 120
b. \t\t6x + y = 68
\t\t3x + 4y = 120
c. \t\t6x + y = 120
\t\t4x + 3y = 68
d. \t\t6x + y = 120
\t\t3x + 4y = 68

Explanation:

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Question 52

Step1: Check non-negative integer requirement

Number of tickets can't be negative or fractional.

Step2: Evaluate each option

• Option A: $x=57$, $y=43$ (positive integers, valid)
• Option B: $x=-57$ (negative, invalid)
• Option C: $x=56.8$, $y=43.1$ (fractional, invalid)
• Option D: $x=56.8$, $y=-43.1$ (fractional/negative, invalid)

Step1: Define variables

Let $x$ = students per van, $y$ = students per bus.

Step2: Set up grade 11 equation

6 vans + 1 bus = 68 students: $6x + y = 68$

Step3: Set up grade 10 equation

4 vans + 3 buses = 120 students: $4x + 3y = 120$

Answer:

A. $x = 57$
$y = 43$

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Question 53