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trapecia [35]
3 years ago
9

A college charters a bus for $1300 to take a group of students to see a Broadway production. When 14 more students join the trip

, the cost per student decreases by $17.50. How many students were in the original group?
Mathematics
1 answer:
tiny-mole [99]3 years ago
6 0
<span>let x = the original no. of students
then
(x+10) = the actual no. that went on the trip
:
 = the original cost per student
and
 = the actual cost 
:
Original cost - actual cost = $12.50
 -  = 12.50
multiply equation by x(x+10)
x(x+10)* - x(x+10)* = 12.50x(x+10)
Cancel the denominators

1500(x+10) - 1500x = 12.5x(x+10)
1500x + 15000 - 1500x = 12.5x^2 + 125x
Combine on the right to form a quadratic equation
0 = 12.5x^2 + 125x - 15000
Simplify, divide equation by 12.5
x^2 + 10x - 1200 = 0
You can use the quadratic formula; a=1; b=10; c=-1200, but this will factor to
(x + 40(x - 30) = 0
The positive solution is what we want here
x = 30 students in the original group
Check this by finding the cost per student for each scenario
1500/30 = $50.00; original cost
1500/40 = $37.50; actual cost
---------------------
saving: $12.50</span>
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Answer:

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Step-by-step explanation:

a. Since Jamie hikes up the mountain at a rate of 300 ft/hr, and the mountain is 1500 ft high, his distance, d from the peak of the mountain at any given time,t  is given by

d = 1500 - 300t.

b.If Jamie distance d = 900 ft, then the equation becomes,

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The equation d = 1500 - 300t. also models his distance from the peak of the  mountain if he hikes down at a constant rate of 300 ft/hr

At d = 900 ft, the equation becomes

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900 - 1500 = -300t

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t = -600/-300

t = 2 hours

So, on his hike down the mountain, it takes him another 2 hours to be 900 ft from the peak of the mountain.

So, he is at 900 ft on his hike down after his start of hiking up the mountain at time t = (2 + 2) hours = 4 hours. Since it takes 2 hours to climb to the peak of he mountain and another 2 hours to climb down 900 ft from the peak of the mountain.

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