Question

The cost of two cushions and three pillows is rupeas 1410.if each cushion costs 200 rupeas more than the pillow,find the cost of cushions and pillows

Answer 1

$\sf\large\underline{Given:}$

$\tt{\implies The\: cost\:_{(2\: cushion+3\: pillow)}=Rs.1410}$

$\sf\large\underline{To\: Find:}$

$\tt{\implies The\: cost\:_{(2\:cushion\:and\:3\:pillow\: separately)}=?}$

$\sf\large\underline{Solution:}$

$\tt{\implies Let,\:The\:cost\:_{(a\:pillow)}=x}$

$\tt{\implies The\:cost\:_{(a\: cushion)}=x+200}$

$\sf\small\underline{According\:to\: above\: information:}$

$\tt{\implies Cost\:_{(2\: cushion)}+Cost\:_{(3\:pillow)}=1410}$

$\tt{\implies 2(x+200)+3(x)=1410}$

$\tt{\implies 2x+400+3x=1410}$

$\tt{\implies 5x+400=1410}$

$\tt{\implies 5x=1410-400}$

$\tt{\implies 5x=1010}$

$\tt{\implies x=202}$

$\sf\large{Hence,}$

$\tt{\implies The\:cost\:_{(a\:cushion)}=(x+200)}$

$\tt{\implies The\:cost\:_{(a\: cushion)}=(202+200)}$

$\bf{\implies The\:cost\:_{(a\: cushion)}=Rs.402}$

$\tt{\implies The\:cost\:_{(a\: pillow)}=x}$

$\bf{\implies The\:cost\:_{(a\: pillow)}=Rs.202}$

$\sf\large\underline{Verification:}$

$\tt{\implies Cost\:_{(2\: cushion)}+Cost\:_{(3\:pillow)}=1410}$

$\tt{\implies 2(x+200)+3(x)=1410}$

$\tt{\implies 2(202+200)+3(202)=1410}$

$\tt{\implies 2(402)+3(202)=1410}$

$\tt{\implies 804+606=1410}$

$\tt{\implies 1410=1410}$

$\sf\large\underline{Hence,\: Verified:}$

Answer 2

S O L U T I O N :

Let the cost of one pillow will be Rs.r

Let the cost of one cushions will be Rs.r + 200

$\underbrace{\sf{According\:to\:the\:question\::}}}}$

$\longrightarrow\sf{2(r+200) + 3(r)=1410}\\\\\longrightarrow\sf{2r+400+3r=1410}\\\\\longrightarrow\sf{2r+3r+400=1410}\\\\\longrightarrow\sf{5r+400=1410}\\\\\longrightarrow\sf{5r=1410-400}\\\\\longrightarrow\sf{5r=1010}\\\\\longrightarrow\sf{r=\cancel{1010/5}}\\\\\longrightarrow\bf{r=Rs.202}$

Thus;

The cost of one pillow is r = Rs.202.

The cost of one Cushions is (r+200) = Rs.(202 + 200) = Rs.402