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If S is 160% of T, then T will be what p...

If S is 160% of T, then T will be what percent of S?

A

0.85

B

0.625

C

0.652

D

0.7

Text Solution

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The correct Answer is:
To solve the problem, we need to find out what percentage T is of S, given that S is 160% of T. Let's break down the solution step by step. ### Step 1: Understand the relationship between S and T We are given that S is 160% of T. This can be expressed mathematically as: \[ S = 160\% \times T \] ### Step 2: Convert the percentage to a fraction To work with this equation, we convert 160% into a fraction: \[ 160\% = \frac{160}{100} = \frac{8}{5} \] Thus, we can rewrite the equation as: \[ S = \frac{8}{5} T \] ### Step 3: Rearrange the equation to find T in terms of S We want to express T in terms of S. To do this, we can rearrange the equation: \[ T = \frac{5}{8} S \] ### Step 4: Calculate what percent T is of S To find out what percentage T is of S, we can express T as a percentage of S: \[ \text{Percentage of } T \text{ of } S = \left( \frac{T}{S} \right) \times 100 \] Substituting the value of T from the previous step: \[ \text{Percentage of } T \text{ of } S = \left( \frac{\frac{5}{8} S}{S} \right) \times 100 \] ### Step 5: Simplify the expression The S in the numerator and denominator cancels out: \[ \text{Percentage of } T \text{ of } S = \left( \frac{5}{8} \right) \times 100 \] ### Step 6: Calculate the final percentage Now, we calculate: \[ \frac{5}{8} \times 100 = 62.5\% \] ### Step 7: Convert percentage to decimal To express this percentage in decimal form, we divide by 100: \[ 62.5\% = 0.625 \] ### Conclusion Thus, T is 0.625 of S, which corresponds to option B.
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