Question

Question #f5a58

Answer 1

8

Explanation:

Let friends be x and bill comes Rs. 1120. So 1 has to pay Rs. 1120/x.

As 3 have no wallets, so ( x - 3 ) friends have to pay Rs. 84 each as an extra. Means Rs (1120/x + 84) each.

Now as per question,
`(1120/x +84)(x-3) = 1120`

`rArr 1120/x. x+84x-3.1120/x-84.3 = 1120`

`rArr 84x - 3360/x = 1120-1120+252`

`rArr 84x^2 -252x-3360 = 0`

`rArr 84(x^2-3x-40) = 0`

`rArr x^2 - 3x - 40 = 0`

`rArr x^2-8x+5x-40 = 0`

`rArr x(x-8)+5(x-8)=0`

`rArr (x-8)(x+5)=0`

`rArr x-8 =0, x+5=0`

x = 8 , -5 [ x cannot be -5]

hence x = 8

SO, TOTAL FRIENDS BE 8

Answer 2

Eight.

Explanation:

This situation can be expressed as the equation

`T = (\frac{T}{P} + E ) (P-3)`

where `T` is the total dinner price, `P` is the number of people and `E` is the extra money.

(Think about this until it makes sense to you. The point of this problem is to practice converting a situation into an equation that models it.)

Each person who is paying is paying what they would have paid if everyone was paying, plus an extra `$84`. That is, each person is paying `\frac{T}{P}` (what they would have paid if the price was evenly divided between the friends), plus some extra amount `E`, so `\frac{T}{P} + E` each in total. To find how much that is collectively, multiply by the number of people paying that much, `P-3`. This should be equal to the total price for the dinner.

From here, simply expand the equation and solve for `P` using the quadratic formula.

`T = (\frac{T}{P} + E ) (P-3)`
`T = T + EP - \frac{3T}{P} - 3E`
`0 = EP - \frac{3T}{P} - 3E`
`0 = EP^2 - 3EP - 3T`

Substitute `E = 84` and `T = 1120` and solve using the quadratic formula for finding roots of equations of the form `ax^2 + bx + c`:

`P = \frac{-b \pm \sqrt{b^2 - 4ac}}{2b}`
`P = \frac{3E \pm \sqrt{9E^2 + 12ET}}{2E}`
`P = \frac{1344}{168}`
`P = 8`