Question 209438: i was assigned this word problem, can you help me solve it? please and thank you.
july 4th 1876, was america's 100th birthday. all members of the family decided to get together for a great family picnic.
when they started off for the picnic grounds, ever wagon they owned was pressed into service. each wagon carried the same number of people.
halfway to the grounds 10 wagons broke down, so it was necessary for the remaining wagons to carry one more person. when they started for home it was discovered that 15 more wagons were out of commission. so in the return trip there were three persons more in each wagon that when they started out in the morning.
the question is: how many people attended the great family picnic?
the paper give you a hint, it says: here's how you might start:
let x = number of people per wagon when they started.
let y = number of wagons when they started
write two equations with x and y, then solve the system. (you'll find that the "xy" terms cancel.)
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! every wagon they owned was pressed into service.
each wagon carried the same number of people.
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Starting number of people is xy
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halfway to the grounds 10 wagons broke down, so it was necessary for the remaining wagons to carry one more person.
xy = (x+1)(y-10)
xy = xy+y-10x-10
y-10x-10 = 0
y - 10x = 10
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when they started for home it was discovered that 15 more wagons were out of commission. so in the return trip there were three persons more in each wagon that when they started out in the morning.
xy = (x+3)(y-25)
xy = xy+3y-25x-75
3y - 25x = 75
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Solve this system of equations:
y - 10x = 10
3y -25x = 75
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Substitute y = 10x+10 into 3y-25x = 75 to solve for "x":
3(10x+10) -25x = 75
30x + 30 -25x = 75
5x = 45
x = 9 (# of people per wagon)
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Substitute into y = 10x+10 to solve for "y":
y = 10*9 + 10 = 100 (# of wagons at the start)
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the question is: how many people attended the great family picnic?
# at the picnic = xy = 9*100 = 900
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Cheers,
Stan H.
Reply to stanbon@comcast.net
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let x = number of people per wagon when they started.
let y = number of wagons when they started
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