is a factory every number math qiestion
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Let the total number of parts be N. Let the original production rate per day be r.
Since 1/3 of the parts are produced at the original rate, that takes N/3r days. The remaining 2N/3 parts are produced at a rate that's 10% higher, that is, 1.1r, which takes 2N/31.1r.
The total time in days to produce these parts is then N/3r+2N/31.1r. Producing all N parts at the original rate would take Nr days. You are told that the new production time is 4 days less, that is,
N/3r+2N/31.1r=Nr−4
Set r = 30 parts per day and rearrange. You have an equation for N
N90+2N99=N30−4
which gives N = 1980 parts when you solve it.
You can then plug everything back in to check that the original production time is 62 days and the new (reduced) production time is 58 days.