Question #f5a58

2 Answers
Sep 19, 2017

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

Sep 19, 2017

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