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Zorluk: OrtaPercentage Calculations

A naval shipyard increases its dry dock maintenance workforce by 12.5%12.5\% to meet new project demands. If the current workforce size after the increase is 810810 personnel, what was the original size of the workforce before the increase?

Cevap: 720 personnel

Cevap

720
The scenario requires a reverse percentage calculation. The final count of 810810 personnel represents the original workforce plus a 12.5%12.5\% increase, meaning 810810 is exactly 112.5%112.5\% (or 98\frac{9}{8}) of the original amount. To find the original amount, you set up the equation 98x=810\frac{9}{8}x = 810 and solve for xx by multiplying 810810 by the reciprocal 89\frac{8}{9}, which equals 720720.

Adım Adım Çözüm

1
Identify the relationship between the final amount and the initial amount.
A 12.5%12.5\% increase means the final amount is 100%+12.5%=112.5%100\% + 12.5\% = 112.5\% of the original amount.
To correctly set up an algebraic representation of the percentage growth based on the unknown starting value.
2
Convert the new percentage multiplier into a fraction.
Knowing that 12.5%=1812.5\% = \frac{1}{8}, the multiplier for a 12.5%12.5\% increase is 1+18=981 + \frac{1}{8} = \frac{9}{8}.
Using fractions makes mental arithmetic much simpler and faster without a calculator.
3
Set up the equation to solve for the original amount.
Letting xx represent the original workforce size, the equation is 98x=810\frac{9}{8}x = 810.
This translates the word problem into a solvable mathematical equation.
4
Solve the equation for xx.
x=810×89=90×8=720x = 810 \times \frac{8}{9} = 90 \times 8 = 720.
Isolating xx provides the initial workforce size before the increase.

Anahtar Kavram

Reverse percentage calculations and percentage-to-fraction conversions.
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Percentage Calculations

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