Question

in a Christmas party each person gives one gift to each other . if total distributed gifts are 90 than how many persons were their in the party?? ​

Answer 1

Step-by-step explanation:

For each person at the party, there are one less gifts given than people.

In other words:

if 2 people were at the party, only 1 present is given per person, for a total of 2 gifts.

If 3 people were at the party, a total of (3)*2 were given for a total of 6 gifts

If 4 people were at the party, a total of (4)*3 were given for a total of 12.

(2)*1 = 2

(3)*2 = 6

(4)*3 = 12

(x+1)*x = 90

(x)(x+1) = 90

x^2 + x = 90

x^2 + x - 90 = 0

Using the quadratic equation:

(-1 + (1-4*-90) ^ (1/2))/2 = 18/2 = 9,

So the total number of people is 9+1=10

To check,

9*10 = 90.

To double check:

If there are 10 people at a party, each person has to give 9 gifts. 10 * 9 is 90.

Answer 2

Answer: 90

Explanation:

Approach-It is the question of a logical reasoning and quadratic equation as well.

Solving way-

Each person present in the party, there are one less gifts given than people.

For example

If 2 people were at the party, only 1 present is given per person, for a total of 2 gifts. or If 3 people were at the party, a total of (3)*2 were given for a total of 6 gifts

In this continuous way-

$(2)*1 = 2(3)*2 = 6(4)*3 = 12(x+1)*x = 90(x)(x+1) = 90x^2 + x = 90x^2 + x - 90 = 0$

Using the quadratic equation:

$(-1 + (1-4*-90) ^ (1/2))/2 = 18/2 = 9,$

Therefore totally number of people is 9+1=10

$9*10 = 90.$

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