word problem?

Question

members of the International Club were to share te $840 cost of a field trip. With 7 members canceld, the cost per member was $4 more.

A.) write an equation to answer this question: How much did each member finally pay for the field trip? Use x to represent the original cost of the trip per member.

B.) Solve the equation and write the answer to the question.

Answer 1

n members originally paid x
n - 7 members finally paid x + 4
Total cost was 840

A) (n - 7)(x + 4) = 840

nx = 840
n = 840/x

(840/x - 7)(x + 4) = 840
840 + 3360/x - 7x - 28 = 840
3360/x - 7x - 28 = 0
3360 - 7x^2 - 28x = 0
480 - x^2 - 4x = 0
x^2 + 4x - 480 = 0

Solve the quadratic
(x + 24)(x - 20) = 0
x = -24 or x = 20

x must be positive so x = 20
Final cost is x + 4

B) Final cost is $24
-----------------------------------------
42 members were originally paying $20 for a total of $840
35 members ended up paying $24 for a total of $840

Answer 2

a) Let x = original cost of the trip per member.
m = original number of members

This means
mx = 840.

Since 7 members cancelled, the cost per member was $4 more. Therefore,

(m - 7)(x + 4) = 840
But, if m = 840/x, then our equation is

(840/x - 7)(x + 4) = 840


b) To solve this equation, we must expand.

840 + 4(840/x) - 7x - 28 = 840

Note that the 840 exists on both sides so they cancel each other out.

4(840/x) - 7x - 28 = 0

Multiply both sides of the equation by x, to get

4(840) - 7x^2 - 28x = 0
3360 - 7x^2 - 28x = 0

Dividing everything by (-7), we get

-480 + x^2 + 4x = 0
x^2 + 4x - 480 = 0

We can factor this as

(x - 20) (x + 24) = 0, which means
x = {20, -24}

We can discard the negative solution since a negative price makes no sense. Therefore,

x = 20

But to write the answer to the question, note that x was equal to the original price (x = 20, or $20.00). What the question is asking for is how much each member finally paid, and this was equal to $4 more than the original price. $20.00 + $4.00 = $24.00

Therefore, each member finally paid $24.00.

Answer 3

let $x be the original cost of the trip per member.
therefore total members before = 840/x
now 7 members are cancelled
therefore total no of members now = (840/x)-7
now cost per member increased by $4
therefore new cost per member equals =$(x+4)
therefore total amount collected after 7 members cancelled = {x+4}{(840/x)-7}
but this amount is equal to $840
therefore equation is
{x+4}{(840/x)-7}=840
on solving u will get
x*840/x +4*840/x -7x - 28 =840
840 + 4*840/x - 7x - 28=840
4*840/x -7x-28 =0
divide by 7
4*120/x - x -4 = 0
multiply by x
4*120 -x^2 - 4x =0
480 - x^2 - 4x =0
x^2 + 4x -480 = 0
x^2 + 24x -20x -480 = 0
x(x+24) -20(x +24) =0
(x-20)(x+24)=0
(x-20)=0 or (x+24) =0
x=20 or x=(-24)
x cannot be negative as money paid by member cannot be negative
therefore x = 20
each member finally pays x+4 = 20 +4 =24
answer:each member finally pay for the field trip=$24
if answer is right vote for me
i know my answer is right

Answer 4

obviously, there were 840/x members initially (as x * no. of members = 840). Now, no. of members = 840/x - 7

So, since each pay x + 4,

(x + 4) ( 840/x - 7) = 840

840 + 3360/x - 7x - 28 = 840
7x^2 + 28x - 3360 = 0

er .. use a calculator to solve the quadratic equation. There will be 1 positive and 1 negative answer. The positive solution is the answer