Question

the cost of 5 pencils and 7 pens is rs 50 and 7 pencils and 5 pens is rs 40 find the cost of one pen and one pencil

solve by elimination methoed​

Answer 1

Answer:

$let : the \: cost \: of \: five \: pencils \: be \: = x \\ cost \: of \: seven \: pens \: be \: = y \\ \\ according \: to \: the \: question \ \\ \\ 5x + 7y = 50 \\ \\ 7x + 5y = 40 \\ \\ by \: elimination \: method \\ \\ 5x + 7y = 50 \: is \: whole \: multipled \: by7 \\ \\ = 35x + 49y = 350 \\ \\ 7x + 5y = 40 \: is \: multiplied \: by \: 5 \\ \\ = 35x + 25y = 200 \\ \\ 35x + 49y = 350 \\ \\ 35x + 25y = 230 \\ \\ \\ 24y = 120 \\ \\ y = \frac{120}{24} \\ \\ divded \: with \: 2table \: \\ \\ \frac{60}{12} \: divided \: with \: 2 \: and \: 6 \: table \\ \\ y = 5 \\ \\ substitutig \: y = 5 \: in \: anyone \: eq \\ \\ 5x + 7(5) = 50 \\ \\ 5x = 50 - 35 \\ \\ 5x = 15 \\ \\ x = 3 \\ \\ \\ there \: for \: no : of \: pencils \: were \: 3 \: and \: no \: of \: pens \: were \: 7$