Question

59 pens and 47 pencils cost Rs 1893, while 47 pens and 59 pencils cost Rs 1605. Find the cost of a pen and that of a pencil.​

Answer 1

1 pen costs = Rs 28.5

1 pencil costs = Rs 4.5

Explanation:

let pen's cost = x

pencil's cost = y

59x + 47y = 1893 Equation1

47x + 59y = 1605 Equation2

multiply Equation1 by -47 and equation2 by 59

-47(59x + 47y = 1893)

-2773x - 2209y = - 88971 Equation3

59(47x + 59y = 1605)

2773x + 3481y = 94695 Equation4

Add Equations 3 and 4

-2773x - 2209y = - 88971

2773x + 3481y = 94695

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1272y = 5724

y = 4.5

to get the value of x, plug in y=4.5 to any of the equations, I use equation1

59x + 47y = 1893

59x + 47(4.5) = 1893

59x + 211.5 = 1893

59x = 1893 - 211.5

59x = 1681.5

x = 28.5