The senior classes at High School A and High School B planned separate trips to the indoor climbing gym. The senior class at High School A rented and filled 14 vans and 1 bus with 137 students. High School B rented and filled 1 van and 2 buses with 85 students. Each van and bus carried the same number of students. Write and solve a system of equations to determine how many students rode in each van and how many students rode in each bus.

Question

The senior classes at High School A and High School B planned separate trips to the indoor climbing gym. The senior class at High School A rented and filled 14 vans and 1 bus with 137 students. High School B rented and filled 1 van and 2 buses with 85 students. Each van and bus carried the same number of students. Write and solve a system of equations to determine how many students rode in each van and how many students rode in each bus.

Answer 1

wow, thank you so much!

Answer 2

I appreciate it, but the answer choices are

9 students per van and 41 students per bus
7 students per van and 39 students per bus
10 students per van and 47 students per bus
11 students per van and 50 students per bus

Answer 3

AAAaannndd the bot gets it wrong yet again!

Equation 1: v + 2b = 85
Equation 2: 14v + b = 137
That gives
7 students per van and 39 students per bus

Answer 4

Use the excerpt from William Howard Taft's Message to Congress, December 3, 1912

The excerpt refers to the use of which type of foreign policy in Sino-American relations in the early 1900s? Explain
A. big stick
B. moral diplomacy
C. dollar diplomacy
D. Roosevelt Corollary

Answer 5

The excerpt from William Howard Taft's Message to Congress, December 3, 1912, refers to the use of C. dollar diplomacy in Sino-American relations in the early 1900s.

In the excerpt, Taft talks about the importance of American trade and investment in China, and how economic ties can help bring stability and progress to the region. The policy of dollar diplomacy was based on the idea that the U.S. should use its economic power to influence foreign policy and promote American commercial interests abroad.

Taft believed that by investing in China's economy, the U.S. could help strengthen the country and prevent its colonization by other European powers. This approach was seen as a shift away from the previous "big stick" policy of Roosevelt and towards a more economic and peaceful form of diplomacy.

Answer 6

Let's start by defining some variables:

Let's call the number of students in each van and bus x.

For High School A:
Number of vans = 14
Number of buses = 1
Total number of students = 137

For High School B:
Number of vans = 1
Number of buses = 2
Total number of students = 85

Now, let's create equations based on the information given:

For High School A:
14x + 1(x) = 137

For High School B:
1x + 2(x) = 85

Let's simplify these equations:

14x + x = 137
15x = 137
x = 137/15

x ≈ 9.133 (approx.)

1x + 2(9.133) = 85
1x + 18.266 ≈ 85
1x ≈ 85 - 18.266
1x ≈ 66.734

x ≈ 66.734 (approx.)

Therefore, each van carried approximately 9 students and each bus carried approximately 66 students.

Answer 7

Let x = number of students in each van

Let y = number of students in each bus

Equation 1: 14x + 2y = 85
Equation 2: x + y = 137

Solving the system of equations:
14x + 2y = 85
x + y = 137

Subtracting equation 2 from equation 1:
13x = 52
x = 4

Substituting x = 4 into equation 2:
4 + y = 137
y = 133

Therefore, 4 students rode in each van and 133 students rode in each bus.