Question

36 pens and 24 pencils together cost rupees 702 while 24 pens and 36 pencils together cost rupees 558 .find the cost of a pen and that of a pencil.​

Answer 1

$\huge\underline{\purple{hello!}}$

hope it helps♡

Answer 2

${\bold{\pink{\underline{\red{So}\purple{lut}\green{ion}\orange{:-}}}}}$

Let the cost of each pen be ₹ x and that of each pencil be ₹ y .

then,

$\rm\:36x+24y=702\:.......................(i)$

$\rm\:24x+36y=558\:.......................(ii)$

$\tt\:On\:adding\:eq(i)\:and\:eq(ii)$

$\rm\:(36x+24y)+(24x+36y)=702+558$

$\rm\implies\:60x+60y=1260$

$\rm\implies\:60(x+y)=1260$

$\rm\implies\:x+y=\cancel\dfrac{1260}{60}$

$\rm\implies\:x+y=21\:........................(iii)$

$\tt\:On\: subtracting\:eq(ii)\:from\:eq(i)$

$\rm\:(24x+36y)-(36x+24y)=702-558$

$\rm\implies\:12x-12y=144$

$\rm\implies\:12(x-y)=144$

$\rm\implies\:x-y=\cancel\dfrac{144}{12}$

$\rm\implies\:x-y=12\:.......................(iv)$

$\tt\:On\:adding\:eq(iii)\:and\:eq(iv)$

$\rm\:(x+\cancel{y})+(x-\cancel{y})=21+12$

$\rm\implies\:2x=33$

$\rm\implies\:x=\dfrac{33}{2}$

$\rm\implies\:x=16.50$

$\tt\:On\: subtracting\:eq(iv)\:from\:eq(iii)$

$\rm\:(\cancel{x}+y)-(\cancel{x}-y)=21-12$

$\rm\implies\:2y=9$

$\rm\implies\:y=\dfrac{9}{2}$

$\rm\implies\:y=4.50$

∴ Cost of each pan will be ₹ 16.50 .

and cost of each pencil will be ₹ 4.50.