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A pen factory signed a contract to produce a number of souvenir pens for a company.

The pen company needs to produce pens in 5 days to accomplish the contract.

On the first day, it produced 1/5 of the required number of pens.
On the second day, it produced another 28 pens,

On the third day, it produced half of the number of pens produced on the first 2 days.

On the fourth day, it produced 9 more pens more than the first day.

On the fifth day, it completed the remaining 64 pens.

How many pens did the factory produce in those 5 days?

 Dec 30, 2021
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Let the total pens produced in 5 days be x.

Pens produced on the first day = x/5

second day = 28

third day = (x/5 + 28)/2

4th day = x/5 + 9

5th day = 64

∴, x/5 + 28 + (x/5 + 28)/2

          + x/5 + 9 + 64

          = x

=> x/5 + 1/2(x/5) + 1/2(28)

        + x/5 + 73 + 28 = x

=> x/5 + x/10 + x/5 + 101 + 14 = x

=> \( {2x + x + 2x \over 10} + 115 = x\)
=> \( {5x + 1150\over 10} = x\)

=> 5x + 1150 = 10x

=>  5x = 1150

=>    x = 230

∴, total pens = \(\boxed{230}\)

 Dec 30, 2021
edited by apsiganocj  Dec 30, 2021

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