Question

The senior classes at Snellville High and General High planned separate trips to the water park. The senior class at Snellville rented and filled 12 vans and 14 buses with 796 students. General High rented and filled 14 vans and 12 buses with 738 students. How many students would fill 2 buses and 3 vans?

Answer 1

133

Explanation:

12V + 14B = 796

6V + 7B = 398 (1)

14V + 12B = 738

7V + 6B = 369 (2)

-7(1) + 6(2)

-42V - 49B = -2786

42V + 36B = 2214

-13B = -572

B = 44

6V + 7(44) = 398

6V = 90

V = 15

2B + 3V

2(44) + 3(15)

88 + 45

133

Answer 2

133

Explanation:

Snellville

12v+14b = 796

General

14v+12b =738

We need to solve for v and b where v is how many on a van and b is how many on a bus

12v+14b = 796

14v+12b =738

Divide each equation by 2

6v+7b =398

7v+6b =369

Multiply the first equation by 7 and the second equation by -6

7(6v+7b) =7(398)

42v +49b =2786

-6(7v+6b) =369*-6

-42v -36b = -2214

Add these equations together

42v +49b =2786

-42v -36b = -2214

-------------------------------

13b = 572

Divide each side by 13

13b/13 = 572/13

b= 44

Now find v

6v+7b =398

6v +7(44)=398

6v +308 = 398

Subtract 308 from each side

6v = 90

Divide by 6

6v/6 = 90/6

v = 15

We want 2 b and 3 v

2b+3v = 2(44)+3(15) = 88+45=133