Out of a group of swans, $\frac{7}{2}$ times the square root of the total number are playing on the share of a pond. The two remaining ones are swinging in water. Find the total number of swans.
Given:
Out of a group of swans, $\frac{7}{2}$ times the square root of the total number are playing on the share of a pond. The two remaining ones are swinging in water.
To do:
We have to find the total number of swans.
Solution:
Let the total number of swans be $x$.
This implies,
Number of swans playing on the share of a pond$=\frac{7}{2}\times \sqrt{x}$
Number of swans swinging in water$=2$.
Therefore,
$x=2+\frac{7}{2}\times \sqrt{x}$
$x-2=\frac{7}{2}\times \sqrt{x}$
$(x-2)^2=(\frac{7}{2}\times \sqrt{x})^2$ (Squaring on both sides)
$x^2-4x+4=\frac{49}{4}x$
$4(x^2-4x+4)=49x$
$4x^2-16x+16-49x=0$
$4x^2-65x+16=0$
Solving for $x$ by factorization method, we get,
$4x^2-64x-x+16=0$
$4x(x-16)-1(x-16)=0$
$(4x-1)(x-16)=0$
$4x-1=0$ or $x-16=0$
$4x=1$ or $x=16$
$x=\frac{1}{4}$ or $x=16$
Therefore, the value of $x$ is $16$. ($x$ cannot be a fraction)
The total number of swans is $16$.
Related Articles
- Half of a herd of a deer are grazing in the field and three fourth of the remaining are playing nearby the rest 9 are drinking water from a pond. Find the number of deer in the herd.
- Half of a herd of deer are grazing in the field and three fourths of the remaining are playing nearby. The rest 9 are drinking water from the pond. Find the number of deer in the herd.
- In a college, out of 4320 students, 2300 are girls. Find the ratio of(a) Number of girls to the total number of students.(b) Number of boys to the number of girls.(c) Number of boys to the total number of students.
- I have a total of rupees 300 in coins of denomination rupees 1, 2, 5 the number of rupees 2 coins is 3 times the number of rupees 5 coins. The total number of coins is 160. Find the number of coins of each denomination.
- The total number of electrons in a nitrogen atom is 7. Find the number of valence electrons in it.
- In an orchard the number of apple trees are $\frac{1}{5}$ of the orchard, number of orange trees are $\frac{3}{13}$ of the orchard and the number of banana trees are 148 in number. What are the total number of trees in the orchard ?
- In a class of 40 students, \( \frac{1}{5} \) of the total number of students like to eat rice only, \( \frac{2}{5} \) of the total number of students like to eat chapati only and the remaining students like to eat both. What fraction of the total number of students like to eat both?
- A school is hosting a story telling competition. A total of $15$ girls participated in the competition. Given that, out of all the participants, $37.5$ % are girls, find the total number of participants.
- Find the Number of \'X\' Total Shapes
- In a class of 52 students, the number of boys is $\frac{ 6}{7}$ of the number of girls find out the number of boys.
- What would be the possible ones digit of the square root of the natural number 6561?
- The number of boys in a class is 5 less than twice the number of girls in the class if the total number of boys is 23 find the total number of students in the class
- 8086 program to find the square root of a perfect square root number
- The sum of a number and its positive square root is $\frac{6}{25}$. Find the number.
- The number of boys and girls in a class are in the ratio 7:5. The number of boys is 8 more than the number of girls. Whar is the total class strength?
Kickstart Your Career
Get certified by completing the course
Get Started