The students at Plymouth South and the students at Plymouth North both planned trips to Six Flags. The students at South rented and filled 2 vans and 11 buses with 674 students. North rented and filled 6 vans and 14 buses with 882 students. Each van and each bus carried the same number of students. Find the number of students each van and In each bus. (Write your answer as an

Number of vans = 7 students

Number of buses = 60 students

Step-by-step explanation:

Let

Number of vans = x

Number of buses = y

2x + 11y = 674 (1)

6x + 14y = 882 (2)

Multiply (1) by 3

6x + 33y = 2,022 (3)

6x + 14y = 882 (2)

Subtract (2) from (3)

33y - 14y = 2,022 - 882

19y = 1,140

y = 1,140 / 19

= 60

y = 60 students

Substitute y = 60 into

2x + 11y = 674 (1)

2x + 11(60) = 674

2x + 660 = 674

2x = 674 - 660

2x = 14

x = 14/2

= 7

x = 7 students

5   1/4   miles per hour

step-by-step explanation:

15   3/4 / 3 = 5   1/4

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3