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15) The senior classes at High School A and High School B planned separate trips to the water park.
The senior class at High School A rented and filled 6 vans and 2 buses with 98 students. High
School B rented and filled 10 vans and 2 buses with 130 students. Every van had the same
number of students in it as did the buses. How many students can a van carry? How many
students can a bus carry?
A) Van: 9, Bus: 26 B) Van: 25, Bus: 8 C) Van: 5, Bus: 22 D) Van: 8, Bus: 25

Sagot :

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Answer:  D) Van: 8, Bus: 25

Bus can carry 25 students ,  van can carry 8 students.

Explanation:

Let vans be v and buses be b

Equations:

6v + 2b = 98 ..........from Theory 1

10v + 2b = 130 ..........from Theory 2

Making b the subject:

6v + 2b = 98

b = (98 - 6v)/2 ............. equation 1

10v + 2b = 130

b = (130 - 10v)/2  .........equation 2

Solving them simultaneously:

(130 - 10v)/2 = (98 - 6v)/2

130 - 10v = 98 - 6v

-6v + 10v = 130 - 98

4v = 32

v = 8

Therefore each van can carry 8 students.

Then the bus can carry: (98 - 6v)/2

                                    → (98 - 6(8))/2

                                    →  25 people

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