Question

37 pens and 53 pencils together cost Rs 320, while 53 pens and 37 pencils together cost Rs 400. find the cost of a pen and that of a pencil.​

Answer 1

☯ Let the cost of a pen be Rs. x and that of a pencil be Rs. y.

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Therefore,

★ According to Question:

37 pens and 53 pencils together cost Rs. 320

➳ 37x + 53y = 320 ....eq (1)

And,

53 pens and 37 pencils together cost Rs. 400

➳ 53x + 37y = 400 ....eq (2)

Adding eq (1) and eq (2),

➳ 90x + 90y = 720

➳ 90(x + y) = 720

➳ x + y = 720/90

➳ x + y = 8 ....eq (3)

Now, Subtracting eq (i) and eq (ii),

➳ 16x - 16y = 80

➳ 16(x - y) = 80/16

➳ x - y = 5 ....eq (4)

Adding eq (iii) and eq (iv),

➳ 2x = 13

➳ x = 6.5

Substituting value of x in eq (iii)

➳ y = (8 - 6.5)

➳ y = 1.5

∴ Hence, cost of one pen is Rs. 6.50 and cost of one pencil is Rs. 1.50.

Answer 2

Answer:

$\bf \implies \large \: let \: the \: value \: of \: pen \: be \: x \\ \\ </p><p> \bf \implies \large \: let \: the \: value \: of \: pencil \: be \: y \\ \\ </p><p> \bf \bull\large 37x \: +53y \: =320..........(1) \\ \\ </p><p> \bf \bull \large \: 53x \: + \: 37y=400..............(2) \\ \\ \\ </p><p> \bf \bull\large on \: multiplying \: eq-1 \: by \: 53 \: and \: eq-2 \: by \: 37 \\ \\ </p><p> \bf \bull \large 1961x+2809y=16960 \\ \\ </p><p> \bf \bull\large 1961x+1369y=14800 \\ \\ </p><p> \bf \implies \large on \: subtracting \\ \\ </p><p> \bf \bullet \: \large \: 1440y=2160 \\ \\ </p><p> \bf \implies \large {\red{ \boxed{ \underline{y=Rs1.5}}}} \\ \\ </p><p> \bf \implies \large so \: x=</p><p>37x+53 \times 1.5=320 \\ \\ </p><p> \bf \implies \large 37x \: + \: 79.5=320 \\ \\ </p><p> \bf \implies \large 37x=320-79.5 \\ \\ </p><p> \bf \implies \large 37x=240.5 \\ \\ </p><p> \sf \large{ \boxed{ \red{x=Rs6.5}}} \\ \\ </p><p> \bf \implies \large so \: cost \: of \: pen \: is \: Rs 6.5 \\ \\ \\ \bf \implies \large cost \: of \: pencil \: is \: Rs 1.5$