SOLUTION: A Senior class is planning a trip to Chicago. a Bus seats 51 people a bus seats 8 people. If there are 150 students going on the trip in a total of 8 vehicles, how many buses and v
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Question 531023: A Senior class is planning a trip to Chicago. a Bus seats 51 people a bus seats 8 people. If there are 150 students going on the trip in a total of 8 vehicles, how many buses and vans are taken on the trip?
I have already found the answer: 2 buses, and 6 vans; but this must be solved algebraically, showing all of my work. How do i do that? (set it up algebraically?) Thank you
Found 2 solutions by oberobic, stanbon:
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
b = number of buses
v = number of vans
51b = number of people carried by each bus
8v = number of people carried by each van
.
51b + 8v = 150 people being carried
.
b + v = 8
so
v = 8-v
.
substitute
.
51b + 8(8-v) = 150
51b + 64 -8v = 150
43b = 86
b = 2
.
v = 8-b
v = 6
.
Check the total people carried.
51(2) = 102
8(6) = 48
102+48 = 150
Correct.
.
Answer: They used 2 buses and 8 vans.
.
Done.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A Senior class is planning a trip to Chicago.
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A bus seats 51 people ; a van seats 8 people. If there are 150 students going on the trip in a total of 8 vehicles, how many buses and vans are taken on the trip?
---------
b + v = 8 vehicles
51b + 8v = 150 students
----
Multiply thru the 1st equation by 8 to get:
8b + 8v = 64
51b + 8v = 150
-----
Subtract and solve for "b":
43b = 86
b = 2 (# of busses)
-----
Solve for "v":
b + v = 8
2 + v = 8
v = 6 (# of vans)
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cheers,
Stan H.
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