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The amount 180.00 is what percent greater than 135.00?

The question aims to find the percent increase in an amount. Percent increase depends on relative change. The relative difference and relative change are used to compare two quantities in consideration of the “size” of what is being compared. Comparisons are expressed as ratios and are unitless numbers. The terms rate of change, percentage (age) difference, or relative percentage difference are also used because these ratios can be expressed as percentages by multiplying them by 100.

Percentage changes are a way of expressing changes in variables. This represents the relative change between the initial and final values.

For example, if a car costs $10,000 today and after a year its costs go up to $11,000, the percentage change in its value can be calculated as

\[\dfrac{11000-10000}{10000}=0.1=10\%\]
There is a $10\%$  increase in the costs of the house after a year.
More generally, $V1$ and $V2$ are the old and new values respectively
\[Percentage\: change=\dfrac{V2-V1}{V1}\times100\%\]

If the variable in the question itself is a percentage, it is advisable to use percentage points to talk about the change to avoid confusion between relative and absolute differences.

Expert Answer

Initial and final values are given in data to find relative change.

The initial smaller amount is given as:

\[vi=\$135.00\]

The final greater amount is given as:

\[vf=\$180.00\]

Percent increase formula is given as:

\[P.I=\dfrac{(vf-vi)}{vi}\times100\]

Substitute values in the above equation:

\[P.I=\dfrac{(180-135)}{135}\times100\]

\[P.I=\dfrac{4500}{135}\times100\]

\[=33.33\%\]

So, the amount of $\$180.00$ is $33.33$ percent greater than $\%135.00$.

Numerical Result

Amount $\$180.00$ is $33.33$ percent greater than $\$135.00$.

Examples

Example 1: The amount $\$190.00$ is what percent greater than $\$120.00$?

The initial smaller amount is given as:

\[vi=\$120.00\]

The final greater amount is given as:

\[vf=\$190.00\]

Percent increase formula is given as:

\[P.I=\dfrac{(vf-vi)}{vi}\times100\]

Substitute values in the above equation:

\[P.I=\dfrac{(190-120)}{120}\times100\]

\[P.I=\dfrac{7000}{120}\times100\]

\[=58.33\%\]

So the amount of $\$190.00$ is $58.33$ percent greater than $\$120.00$.

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