Question

At a carnival, 1/10 of the balloons burst and 35% of the balloons were given to some children. There were 220 balloons left. How many balloons were there at first?

Answer 1

Given :-

▪ At a carnival, 1/10 of the balloons burst and 35% were given to some children. There were 220 balloons left.

To Find :-

▪ Number of balloons that were there first.

Solution :-

Let the number of balloons that were there at first be x .

It is given that 1/10 of the balloons were burst or x / 10 balloons and 35% of the balloons was given to children or simply 35x / 100 balloons.

According to the question,

⇒ Total balloons - (Number of balloons that burst + Number of balloons that were given to the children) = 220

⇒ x - (x/10 + 35x/100) = 220

⇒ x - { (10x + 35x) /100 } = 220

⇒ x - 45x / 100 = 220

⇒ ( 100x - 45x ) / 100 = 220

⇒ 55x = 22000

⇒ x = 400

Hence, There were 400 balloons at first.

Answer 2

GIVEN :-

• Aᴛ ᴀ ᴄᴀʀɴɪᴠᴀʟ, $\bf\red{\dfrac{1}{10}}$ ᴏғ ᴛʜᴇ ʙᴀʟʟᴏᴏɴs ʙʀᴜsᴛ .

• Aɴᴅ 35% ᴡᴇʀᴇ ɢɪᴠᴇɴ ᴛᴏ sᴏᴍᴇ ᴄʜɪʟᴅʀᴇɴ .

• Tʜᴇʀᴇ ᴡᴇʀᴇ 220 ʙᴀʟʟᴏᴏɴs ʟᴇғᴛ .

TO FIND :-

• Nᴏ. ᴏғ ʙᴀʟʟᴏᴏɴs ᴛʜᴀᴛ ᴡᴇʀᴇ ᴛʜᴇʀᴇ ғɪʀsᴛ .

SOLUTION :-

ʟᴇᴛ,

• Tʜᴇ ɴᴏ. ᴏғ ʙᴀʟʟᴏᴏɴs ᴛʜᴀᴛ ᴡᴇʀᴇ ᴛʜᴇʀᴇ ᴀᴛ ғɪʀsᴛ ʙᴇ "X" .

Aᴄᴄᴏʀᴅɪɴɢ ᴛᴏ ᴛʜᴇ ǫᴜᴇsᴛɪᴏɴ,

ᴄᴀsᴇ - 1 :-

☯︎ ɴᴏ. ᴏғ ʙʀᴜsᴛ ʙᴀʟʟᴏᴏɴs :-

• $\bf\blue{\dfrac{X}{10}}$ ʙᴀʟʟᴏᴏɴs .

ᴄᴀsᴇ - 2 :-

☯︎ ɴᴏ. ᴏғ ʙᴀʟʟᴏᴏɴs ɢɪᴠᴇɴ ᴛᴏ ᴄʜɪʟᴅʀᴇɴ :-

• $\bf\blue{\dfrac{35}{100}\:X\:}$ ʙᴀʟʟᴏᴏɴs .

ᴄᴀsᴇ - 3 :-

☯︎ ᴛʜᴇʀᴇ ᴡᴇʀᴇ 220 ʙᴀʟʟᴏᴏɴs ʟᴇғᴛ .

$\bf{:\implies\:X\:-\:\Big[\:\dfrac{X}{10}\:+\:\dfrac{35}{100}\:X\:\Big]\:=\:220\:}$

$\rm{:\implies\:X\:-\:\Big[\:\dfrac{10X\:+\:35X}{100}\Big]\:=\:220\:}$

$\rm{:\implies\:X\:-\:\dfrac{45X}{100}\:=\:220\:}$

$\rm{:\implies\:\dfrac{100X\:-\:45X}{100}\:=\:220\:}$

$\rm{:\implies\:55X\:=\:220\times{100}\:}$

$\rm{:\implies\:X\:=\:\dfrac{22000}{55}\:}$

$\bf\green{:\implies\:X\:=\:400\:}$

$\huge\red\therefore$ Nᴏ. ᴏғ ʙᴀʟʟᴏᴏɴs ᴛʜᴀᴛ ᴡᴇʀᴇ ᴛʜᴇʀᴇ ғɪʀsᴛ ɪs "400" .