SOLUTION: A group of friends go out for supper one evening. They decide to share the bill which comes to R960. However, two of them forget their wallets and cannot pay. The remaining friends

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Question 1160735: A group of friends go out for supper one evening. They decide to share the bill which comes to R960. However, two of them forget their wallets and cannot pay. The remaining friends each now have to pay an extra R40 to cover the cost. How many friends are in the group?
Found 3 solutions by ankor@dixie-net.com, josgarithmetic, MathTherapy:
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website!
A group of friends go out for supper one evening.
They decide to share the bill which comes to R960.
However, two of them forget their wallets and cannot pay.
The remaining friends each now have to pay an extra R40 to cover the cost.
How many friends are in the group?
:
let x = no. of friends
then
(x-2) = no. that paid
and
= amt paid if each paid their share
:
- 40 =
multiply by x(x-2)
960x - 40x(x-2) = 960(x-2)
960x - 40x^2 + 80x = 960x - 1920
subtract 960x from both side
-40x^2 + 80x + 1920 = 0
simplify, divide by -40
x^2 - 2x - 48 = 0
Factors to
(x-8)(x+6) = 0
positive solution
x = 8 friends
:
:
Check this
If all paid: 960/8 = 120
If six paid: 960/6 = 160
-------------------------
6 friends ea pd more: 40, total of 240 to cover 2 unpaying friends
-

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

n, unknown number of friends in the group

I assume here that EACH paying friend had to pay an extra R40.

PRICE PERSONS COST ALL FRIENDS 960/n n 960 TWO NOT PAY 960/(n-2) n-2 960 DIFFERENCE 40

--------simplify and solve this for n.

Answer by MathTherapy(10552)   (Show Source):
You can put this solution on YOUR website!

A group of friends go out for supper one evening. They decide to share the bill which comes to R960. However, two of them forget their wallets and cannot pay. The remaining friends each now have to pay an extra R40 to cover the cost. How many friends are in the group?

Let number of friends be N
Then each friend's share should have been:
With 2 friends not being able to pay, then number who were able to pay was: N - 2, and those who could pay then needed to pay:
We then get:
----- Reducing fractions by factoring out GCF, 40, in numerator
24(N - 2) = 24N - N(N - 2) ------ Multiplying by LCD, N(N - 2)

(N - 8)(N + 6) = 0
Number of friends, or OR N = - 6 (ignore)