SOLUTION: The Extreme Rock Climbing Club planned a climbing expedition. The total cost was $1200 , which was to be divided equally among the members going. Prior to the trip, 3 members

Question 1201163: The Extreme Rock Climbing Club planned a climbing expedition. The total cost was $1200
, which was to be divided equally among the members going. Prior to the trip, 3
members decided not to go. If the cost per person increased by $90
, how many people went on the expedition?

Found 3 solutions by greenestamps, josgarithmetic, ikleyn:
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

You can find the answer quickly using trial and error and simple arithmetic.Since the problem says the cost increased after 3 people decided not to go, the original number of people was greater than 3. Make a list of the cost per person for different numbers of people in the group and look for places where the number of people differs by 3 and the cost per person differs by 90.
# people cost per person -------------------------- 4 1200/4 = 300 5 1200/5 = 240 6 1200/6 = 200 8 1200/8 = 150

The original group was 8 people paying $150 each; the final group was 8-3=5 people paying $150+$90=$240 each.

But presumably you wanted an algebraic solution....

Here is one way you can do it.

Let x be the original number of people
let y be the original cost per person

The $1200 was originally x people paying y dollars each; that same $1200 was (x-3) people paying (y+90) dollars each:

Substitute this expression for y in the first equation:

( makes no sense)

ANSWER: The number of people who went on the expedition was x-3 = 8-3 = 5

Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!

PRICE PERSONS COST 1200/n n 1200 1200/(n-3) n-3 1200 diff. 90

Price per person not given; question asks for how many persons went.
Using here, n for how many people planned to go.
Not really need a specific variable just for price.

-------simplify and solve.
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
The Extreme Rock Climbing Club planned a climbing expedition. The total cost was $1200,
which was to be divided equally among the members going. Prior to the trip, 3 members
decided not to go. If the cost per person increased by $90, how many people went on the expedition?
~~~~~~~~~~~~~~~~~~~~

Let n be the number of people went on the expedition. The number of the members originally was (n+3). The price per a member originally was . The price per a person finally was . The difference of prices is $90 (given), which gives us this "price" equation - = 90. (1) +------------------------------------------+ | At this point, the setup is complete. | | Now our goal is to solve the equation. | +------------------------------------------+ To do it, first simplify it by dividing both sides by 30. You will get - = 3. (2) At this point, you just can to "guess" the answer MENTALLY: it is n= 5. But let's do it formally. From (2), multiplying both sides by n*(n+3), you get 40*(n+3) - 40n = 3n*(n+3), 40n + 120 - 40n = 3n*(n+3), 120 = 3n(n+3), 40 = n*(n+3), n^2 + 3n - 40 = 0. Factor left side (n+8)*(n-5) = 0. There are two roots, n= -8 and n= 5. According to the meaning of the problem, n= 5 is a meaningful solution while n= -8 is not, so we reject it. ANSWER. 5 persons went on the expedition.

Solved.

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