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Difficulty: MediumPercentage Calculations

During a physical fitness assessment, 6868 recruits met the advanced standard. If these recruits represent 17%17\% of the total training company, what is the total number of recruits in the company?

Answer: 400 recruits

Answer

400
The correct total is found by recognizing the relationship: Part=Rate×Base\text{Part} = \text{Rate} \times \text{Base}. We are given the Part (6868) and the Rate (17%17\% or 0.170.17). To find the Base, we divide the Part by the Rate: 68÷0.17=40068 \div 0.17 = 400.

Step-by-Step Solution

1
Set up an algebraic equation relating the given part to the unknown whole.
0.17×x=680.17 \times x = 68
The problem states that 17%17\% of the total class (xx) is equal to 6868 recruits.
2
Isolate the variable xx to solve for the total.
x=680.17x = \frac{68}{0.17}
Dividing both sides of the equation by 0.170.17 will leave xx by itself.
3
Perform the division without a calculator.
x=400x = 400
Multiply the numerator and denominator by 100100 to remove the decimal, resulting in 680017\frac{6800}{17}. Since 17×4=6817 \times 4 = 68, 680017\frac{6800}{17} equals 400400.

Key Concept

Finding the original base when a percentage rate and its corresponding amount are known.
Estimated Time:1m 0s
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Topics

Percentage Calculations

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