Question

Un grupo de amigos toman un refresco cada uno y deben pagar 9 € por el total de las consumiciones. Como hay dos que solo pueden poner 1 €, los demás deben aumentar su aportación en 0,25 € cada uno. ¿Cuántos amigos son?

Answer 1

To find the number of friends, we can set up an equation. The equation is 2 € + (x - 2) * (0.25 €) = 9 € where x represents the total number of friends. Solving the equation gives x = 30, so there are 30 friends in total.

Step-by-step explanation:

To solve this problem, we can set up an equation. Let's say there are x friends in total. The two friends who can only contribute 1 € contribute a total of 2 €. The remaining x-2 friends need to increase their contribution by 0.25 € each. So, their combined contribution is (x - 2) * (0.25 €). The total amount contributed by all friends is 9 €. Therefore, the equation becomes:

2 € + (x - 2) * (0.25 €) = 9 €

Simplifying this equation, we get:

2 € + 0.25x - 0.5 € = 9 €

0.25x + 1.5 € = 9 €

0.25x = 7.5 €

x = 30

So, there are 30 friends in total.

Answer 2

6 friends (4 pay € 1.75 and 2 pay € 1)

Step-by-step explanation:

We have to:

x = friends

y = payment

x * y = 9

y = 9 / x

It follows from the problem:

(x-2) * (y + 0.25) = 9 - 2

(x-2) * (9 / x + 0.25) = 7

x * 9 / x + 0.25 * x - 2 * 9 / x - 2 * 0.25 = 7

9 + 0.25 * x - 18 / x - 0.5 = 7

multiply by 100

100 * 0.25 * x - 100 * 18 / x + 100 * (9 - 0.5 - 7) = 0

25 * x - 1800 / x + 150 = 0

multiply by x

25 * x ^ 2 + 150 * x - 1800 = 0

we factor:

(x - 6) * (x + 12) = 0

x = 6

x = -12

The positive value is taken: x = 6

Each one had to pay = 9/6 = € 1.5

But as two pay € 1, 4 will pay € 0.25 more: 1.5 +0.25 = € 1.75

Thus :

(4 * 1.75) +2 (1) = € 9

Therefore, they are 6 friends (4 pay € 1.75 and 2 pay € 1)