Question

There are 100 mangoes in a gampa, the population is 100, one man gives four teeth, one woman two teeth, four children one fruit, but how many men, women and children?

Answer 1

Let the number of men and women are x and y respectively.

Then the number of children be 100 - (x + y).

By the given condition,

4x + 2y + {100 - (x + y)}/4 = 100

or, 16x + 8y + 100 - x - y = 400

or, 15x + 7y = 300

So we have only one equation with two unknown variables.

We can write: x = (300 - 7y)/15

However we can find values by consideration.

We can find a set of results:

y x

0 20

15 13

30 6

45 - 1

Here y = 0 and x = - 1 are not possible.

We take the possible values

x = 13, y = 15 and x = 6, y = 30

Answer:

• Number of men = 13
• Number of women = 15
• Number of children = 72

OR,

• Number of men = 6
• Number of women = 30
• Number of children = 64

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Answer 2

Given data:

• According to the given question, there are 100 mangoes in a basket.
• The population is 100 people.
• However, one gave four fruits to a man, two fruits to a woman, and one fruit to four children.

To find:

How many men, women, and children were there?

Solution:

For a while, the total number of men who took the fruits be 'x' and the number of females be 'y'.

Then, the number of children becomes 100 - (x + y).

The equation that comes when these are arranged in the order given is:

4x + 2y + [(100 - (x + y)) / 4] = 100

16x + 8y + 100 - x - y = 100 * 4

15x + 7y = 400 - 100

15x + 7y = 300

The rephrased equation will be

x = (300 - 7y) / 15

Since there are two unknown variables ​​here, we need to see which values ​​should be placed in the 'y' position, such that the equation is completely divided and gives a natural number as an output.

The resulting x,y pairs are: [without 0]

If y = 15 then x = 13.

If y = 30 then x = 6.

On substitution, the possible answers that we found here are:

Answer 1:

Number of females: 15

Number of males: 13

Number of children: 72

Or

Answer 2:

Number of females: 30

Number of males: 6

Number of children: 64

Learn more:

1. There are 100 mangoes in a gampa, the population is also 100, one is given four teeth per man, two teeth per woman, one fruit per four children, but how many men, women, and children? A calculation for a while of fun

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2. There are 100 mangoes in a gampa, the population is 100, one man gives four teeth, one woman two teeth, four children one fruit, but how many men, women, and children?

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