SOLUTION: Bill and a group of friends decided to rent a house in Aspen Colorado for a week of skiing. They each had to chip in $90 for the week lodging. If they had been able to convince thr

Question 806043: Bill and a group of friends decided to rent a house in Aspen Colorado for a week of skiing. They each had to chip in $90 for the week lodging. If they had been able to convince three more people to go, the cost per person would have been reduced by $15. What was the rent for the house for the week?
Found 3 solutions by ankor@dixie-net.com, mananth, josgarithmetic:
Answer by ankor@dixie-net.com(22740)   (Show Source): You can put this solution on YOUR website!
They each had to chip in $90 for the week lodging.
If they had been able to convince three more people to go, the cost per person would have been reduced by $15.
What was the rent for the house for the week?
:
let r = total rent for the house for the week
then
= actual amt paid be each person
and cost with additional people 90-15 = 75
= amt if 3 more people join them
:
+ 3 =
multiply by 450 to clear the denominators
450* + 3(450) = 450*
cancel
5r + 1350 = 6r
1350 = 6r - 5r
r = $1350 is the weekly rent
:
:
See if that works, find the number of people
1350/90 = 15 people
1350/75 = 18 people, 3 more

Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!
let the number of friends be x
rent for week = 90x
If 7 join
they total x+7
each has to pay
90x/(x+7) = 75
90x=75(x+7)
90x=75x+525
15x= 525
/15
x=35
Rent = 35*90= 3150

Answer by josgarithmetic(39621)   (Show Source): You can put this solution on YOUR website!
Let j = the group of friends, as a whole number for the $90/week from each person. The rent for the house is , units of dollars per week per person.

THREE MORE PEOPLE?
(j+3) group of friends, expecting then $(90-15) per person for the rental.
The house rent would be the same, but 75*(j+3) is now the rent expression for this increased quantity of friends. Again, the house rent rate itself IS STILL THE SAME.

Find j, the number of people in the group.

Rent rate for the house for the week: dollars
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