Yuan Ling had some $5 and $10 notes. The $5 and $10notes had a total value of $1260.

8 pieces of $10 notes were exchanged for $5notes for the same value. In the end, the number of $10 notes was the same as the $5 notes. What was the value of the $5 notes at first?

Ankita Agarwal answered this

Dear Student,

$Letthenumberof5notedbexandnumberof10notesbey.\phantom{\rule{0ex}{0ex}}Then,5x+10y=1260\phantom{\rule{0ex}{0ex}}Accordingtoquestion,5\left(x+16\right)+10\left(y-8\right)=1260....\left(1\right)\phantom{\rule{0ex}{0ex}}Also,x=y\phantom{\rule{0ex}{0ex}}Substitutingx=yinequ.\left(1\right)\phantom{\rule{0ex}{0ex}}5x+80+10x-80=1260\phantom{\rule{0ex}{0ex}}15x=1260\phantom{\rule{0ex}{0ex}}x=\frac{1260}{15}\phantom{\rule{0ex}{0ex}}x=84\phantom{\rule{0ex}{0ex}}Hence,thereare84notesof5.\phantom{\rule{0ex}{0ex}}Henceatstartingtherewere\left(84-16\right)=68notesof5\phantom{\rule{0ex}{0ex}}Valueof5notes=68\times 5=Rs340$

Regards

$Letthenumberof5notedbexandnumberof10notesbey.\phantom{\rule{0ex}{0ex}}Then,5x+10y=1260\phantom{\rule{0ex}{0ex}}Accordingtoquestion,5\left(x+16\right)+10\left(y-8\right)=1260....\left(1\right)\phantom{\rule{0ex}{0ex}}Also,x=y\phantom{\rule{0ex}{0ex}}Substitutingx=yinequ.\left(1\right)\phantom{\rule{0ex}{0ex}}5x+80+10x-80=1260\phantom{\rule{0ex}{0ex}}15x=1260\phantom{\rule{0ex}{0ex}}x=\frac{1260}{15}\phantom{\rule{0ex}{0ex}}x=84\phantom{\rule{0ex}{0ex}}Hence,thereare84notesof5.\phantom{\rule{0ex}{0ex}}Henceatstartingtherewere\left(84-16\right)=68notesof5\phantom{\rule{0ex}{0ex}}Valueof5notes=68\times 5=Rs340$

Regards