Question

the senior classes at ms 172 and ms 210 planned separate trips to the math moma in manhattan. the senior class at ms 172 rented and filled 1 van and 6 buses with 372 students. ms 210 rented and filled 4 vans and 12 buses with 780 students. each van and each bus carried the same number of students. if ms 311, wishes to join them at the math moma. this school has rented 14 vans and 8 buses for their trip. how many senior students are at ms 311? do not forget to start with let x = number of students in a bus let y= number of students in a van

Explanation:

Step1: Set up equations from given info

From MS 172: \( y + 6x = 372 \)
From MS 216: \( 4y + 12x = 780 \)

Step2: Simplify the second equation

Divide \( 4y + 12x = 780 \) by 4: \( y + 3x = 195 \)

Step3: Subtract equations to solve for x

Subtract \( y + 3x = 195 \) from \( y + 6x = 372 \):
\( (y + 6x) - (y + 3x) = 372 - 195 \)
\( 3x = 177 \)
\( x = \frac{177}{3} = 59 \)

Step4: Substitute x to find y

Plug \( x = 59 \) into \( y + 3x = 195 \):
\( y + 3(59) = 195 \)
\( y + 177 = 195 \)
\( y = 195 - 177 = 18 \)

Step5: Calculate MS 311's students

MS 311 has 14 vans and 8 buses:
Total = \( 14y + 8x \)
Substitute \( x = 59 \), \( y = 18 \):
\( 14(18) + 8(59) = 252 + 472 = 724 \)

Answer:

724