Question

ᴛʜᴇ sᴛᴜᴅᴇɴᴛs ᴏғ ᴀ ᴄʟᴀss ᴀʀᴇ ᴍᴀᴅᴇ ᴛᴏ sᴛᴀɴᴅ ɪɴ ʀᴏᴡs. ɪғ 3 sᴛᴜᴅᴇɴᴛs ᴀʀᴇ ᴇxᴛʀᴀ ɪɴ ᴀ ʀᴏᴡ ᴛʜᴇʀᴇ ᴡᴏᴜʟᴅ ʙᴇ 1 ʀᴏᴡ ʟᴇss. ɪғ 3 sᴛᴜᴅᴇɴᴛs ᴀʀᴇ ʟᴇss ɪɴ ᴀ ʀᴏᴡ, ᴛʜᴇʀᴇ ᴡᴏᴜʟᴅ ʙᴇ ᴛᴡᴏ ʀᴏᴡs ᴍᴏʀᴇ.
ғɪɴᴅ ᴛʜᴇ ɴᴜᴍʙᴇʀ ᴏғ sᴛᴜᴅᴇɴᴛs ɪɴ ᴛʜᴇ ᴄʟᴀss.

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Answer 1

ʟᴇᴛ ᴛʜᴇ ɴᴜᴍʙᴇʀ ᴏғ ʀᴏᴡs ʙᴇ x ʀᴏᴡs ᴀɴᴅ ᴛʜᴇ ɴᴜᴍʙᴇʀ ᴏғ sᴛᴜᴅᴇɴᴛs ɪɴ ᴇᴀᴄʜ ʀᴏᴡ ʙᴇ ʏ sᴛᴜᴅᴇɴᴛs .

ᴛʜᴇɴ ᴛʜᴇ ᴛᴏᴛᴀʟ ɴᴜᴍʙᴇʀ ᴏғ sᴛᴜᴅᴇɴᴛs ɪɴ ᴀ ᴄʟᴀss =xʏ sᴛᴜᴅᴇɴᴛs.

∴ ᴀᴄᴄᴏʀᴅɪɴɢ ᴛᴏ ᴛʜᴇ ǫᴜᴇsᴛɪᴏɴ ,

(x−2)(ʏ+1)=xʏ

⇒xʏ+x−2ʏ−2=xʏ

x−2ʏ=2⟶(ɪ)

ᴀɴᴅ

(x+3)(ʏ−1)=xʏ

⇒xʏ−x+3ʏ−3=xʏ

−x+3ʏ=3⟶(ɪɪ)

x−2ʏ=2

−x+3ʏ=3

ᴏɴ ᴀᴅᴅɪɴɢ , ʏ=5 sᴛᴜᴅᴇɴᴛs.

ᴘᴜᴛᴛɪɴɢ ᴛʜᴇ ᴠᴀʟᴜᴇ ᴏғ ʏ ɪɴ ᴇǫᴜᴀᴛɪᴏɴ ⟶(ɪ)

x−2(5)=2

x=12 ʀᴏᴡs.

∴ ᴛᴏᴛᴀʟ ɴᴜᴍʙᴇʀ ᴏғ sᴛᴜᴅᴇɴᴛs ɪɴ ᴀ ᴄʟᴀssʀᴏᴏᴍ =(12×5)sᴛᴜᴅᴇɴᴛs =60 sᴛᴜᴅᴇɴᴛs.

ʜᴇʀᴇ ɪs ᴜʀ ᴀɴsᴡᴇʀ . ɴᴏ sᴘᴀᴍᴍɪɴɢ ᴅᴏɴᴇ ʙʏ ᴍᴇ . :)