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Kazeer [188]
2 years ago
12

New York City is a popular field trip destination. THis year the senior class at High School A and the senior class at High Scho

ol B both planned trips there. The senior class at High School A rented and filled 1 van and 6 buses with 324 students. High School B rented and filled 9 van and 3 busses with 264 students. How many students can a van carry? How many students can a bus carry?
Mathematics
2 answers:
maw [93]2 years ago
8 0

Answer:

number of students in a van=12

number of students in a bus=52

Step-by-step explanation:

let number of students in a van=x

number of students in a bus=y

1x+6y=324     ...(1)

9x+3y=264   ...(2)

multiply (2) by 2

18x+6y=528   ...(3)

(3)-(1) gives

17x=204

x=204/17=12

put in (1)

12+6y=324

6y=324-12=312

y=312/6=52

Vinil7 [7]2 years ago
6 0

Answer:

number of students in a van=12

number of students in a bus=52

Step-by-step explanation:

let a number of students in a van=x

number of students in a bus=y

1x+6y=324 ...(1)

9x+3y=264 ...(2)

multiply (2) by 2

18x+6y=528 ...(3)

(3)-(1) gives

17x=204

x=204/17=12

put in (1)

12+6y=324

6y=324-12=312

y=312/6=52

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Answer:

The correct option is;

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Step-by-step explanation:

The given expression is presented as follows;

\sum\limits _{n = 1}^{50}n\times \left (4\cdot n + 3  \right )

Which can be expanded into the following form;

\sum\limits _{n = 1}^{50} \left (4\cdot n^2 + 3  \cdot n\right ) = 4 \times \sum\limits _{n = 1}^{50} \left  n^2 + 3  \times\sum\limits _{n = 1}^{50}  n

From which we have;

\sum\limits _{k = 1}^{n} \left  k^2 = \dfrac{n \times (n+1) \times(2n+1)}{6}

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Therefore, substituting the value of n = 50 we have;

\sum\limits _{n = 1}^{50} \left  k^2 = \dfrac{50 \times (50+1) \times(2\cdot 50+1)}{6}

\sum\limits _{k = 1}^{50} \left  k = \dfrac{50 \times (50+1) }{2}

Which gives;

4 \times \sum\limits _{n = 1}^{50} \left  n^2 =  4 \times \dfrac{n \times (n+1) \times(2n+1)}{6} = 4 \times \dfrac{50 \times (50+1) \times(2 \times 50+1)}{6}

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Therefore, we have;

4 \left (\dfrac{50 (50+1) (2\times 50+1)}{6} \right ) +3  \left (\dfrac{50(51) }{2} \right ).

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