The local amusement park is a popular field trip destination. this year the senior class at high school a and the senior class at high school b both planned trips there. the senior class at high school a rented and filled 6 vans and 10 buses with 376 students. high school b rented and filled 3 vans and 2 buses with 104 students. each van and each bus carried the same number of students. how many students can a van carry? how many students can a bus carry?

Number of students can a van  carry are 16 and number of students can a bus carry are 28 .

Step-by-step explanation:

The number of students a van carry be x .

The number of students a bus carry be y .

As given

The local amusement park is a popular field trip destination.

This year the senior class at High School A and the senior class at High School B both planned trips there.

The senior class at High School A rented and filled 6 vans and 10 buses with 376 students.

Equations becomes

6x + 10y = 376

As given

High School B rented and filled 3 vans and 2 buses with 104 students.

Equations becomes

3x + 2y = 104

Multiply 3x + 2y = 104 by 2 and subtracted from 6x + 10y = 376 .

6x - 6x + 10y - 4y = 376 - 208

6y = 168

y = 28

Putting the value of y in the equation 3x + 2y = 104 .

3x + 28 × 2 = 104

3x + 56 = 104

3x = 104 - 56

3x = 48

x = 16

Therefore the number of students can a van  carry are 16 and number of students can a bus carry are 28 .

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)

n=9

step-by-step explanation:

7 times a number = 7n

decreased by 13 = 7n-13

same as is =

5 times the number = 5n

increased by 5 = 5n+5

7n-13 = 5n+5

2n=18

n=9