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The proportional relationship 15.24 centimeters in 6 inches is represented by 6y = 15.24x. Determine the number of centimeters in 1 inch.

A. 2.54 centimeters
B. 3 centimeters
C. 0.39 centimeters
D. 91.44 centimeters

3 answers

To determine the number of centimeters in 1 inch from the equation given, we can start by rewriting the equation.

The equation provided is:

\[ 6y = 15.24x \]

Here, \(y\) represents the number of centimeters and \(x\) represents the number of inches. To find the constant ratio (the number of centimeters in 1 inch), we can solve for \(y\) when \(x = 1\):

  1. Substitute \(x = 1\):

\[ 6y = 15.24(1) \]

\[ 6y = 15.24 \]

  1. Now, solve for \(y\):

\[ y = \frac{15.24}{6} \]

  1. Calculating this gives:

\[ y = 2.54 \]

Thus, the number of centimeters in 1 inch is:

A. 2.54 centimeters

are you sure this is correct

Yes, the calculation is correct. Let’s go through it step by step again for clarity.

The initial equation given is:

\[ 6y = 15.24x \]

Where:

  • \(y\) is the number of centimeters,
  • \(x\) is the number of inches.

To find out how many centimeters are in 1 inch, we set \(x = 1\):

  1. Substitute \(x = 1\) into the equation:

\[ 6y = 15.24(1) \]

This simplifies to:

\[ 6y = 15.24 \]

  1. Now, to solve for \(y\), divide both sides by 6:

\[ y = \frac{15.24}{6} \]

Calculating this gives:

\[ y = 2.54 \]

So, indeed, the conclusion is that there are 2.54 centimeters in 1 inch. Therefore, the answer is:

A. 2.54 centimeters.