Math Word Problem..help please...Algebra..?

Question

Ski Trip
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A Group of Friends decide to rent a house in ASpen, Colorado, for a week of skiing. They each had to chip in $70 for the weeks lodging. If they had been able to convince three more people to go, the cost per person would have been reduced by $14. What was the rent for the week?

try her out.. I can't figuer it out??

Answer 1

The total rent would be the same if there were "p" number of persons, each paying $70, or "p + 3" number of persons, each paying $70 - $14. Sooooooo...

p * 70 = (p + 3) * (70 - 14) = total rent
70p = (p + 3) * 56
70p = 56p + 168
70p - 56p = 168
14p = 168
p = 12
since p * 70 = total rent, 12 * 70 = total rent = $840

Answer 2

Let x be the total rent
If n is the number of friends that went, then
n friends * $70/friend = x
But n+3 friends * ($70-14) = x
Since x = x
70 n = 56(n+3) = 56n + 168
(70-56) n = 168
14n = 168
n = 168/14 = 12 friends
x = $70/friend * 12 friends = $70(12) = $840

Answer 3

a=total rent
b=number of people

a/b=70 => a=70b
a/(b+3)=70-14=56 => a=(b+3)*56 => a=56b+168

thus

70b=56b+168 => 14b=168 => b=12

then

a=70*12=840.

The rent was $840.

Check it=> 840/12 = 70 and 840/15 = 56 = 70-14

Word.

Answer 4

x*$70 = Cost
(x+3) * $(70-14) = Cost

Equate them

70x = 56 (x+3)
70x=56x + 168
14x=168
x=12

12*$70 = $840

Answer 5

let total money to pay = T
number of ppl =x
so 1st case :
each person pays 70
which is equal to T/x=70
2nd case :
each person pays 70-14 =56
which is equal to T/(x+3)=56
now we have 2 equations in 2 unkowns easy to solve
x=12
T=840$