Chapter 6.4, Problem 39STP

To determine

To find: Which statement is supported by the table.

Answer to Problem 39STP

The budget increased $20\%$ from $2011$ to $2012$

Explanation of Solution

Given information:

The table shows the budget of a city.

Percent of change $=\frac{A}{O}\times 100$

Where

  $A=$ Amount of change.

  $O=$ Original amount.

From given information

Budget in $2009$

  $=45.6$ millions of $.

Budget in $2010$

  $=48.3$ millions of $.

Amount of change $=$ Budget in $2010$

  $-$ Budget in $2009$

  $\begin{array}{l}\Rightarrow A=48.3-45.6\\ \Rightarrow A=2.7\end{array}$

Percent of change $=\frac{2.7}{45.6}\times 100$

  $\Rightarrow$ Percent of change $=\frac{270}{45.6}$

  $\Rightarrow$ Percent of change $=5.921$

Therefore,

Percent of change is $5.921\%$ from budget in $2009$ to budget in $2010$ and positive sign indicates percent of increase.

From given information

Budget in $2010$

  $=48.3$ millions of $.

Budget in $2011$

  $=45.9$ millions of $.

Amount of change $=$ Budget in $2011$

  $-$ Budget in $2010$

  $\begin{array}{l}\Rightarrow A=45.9-48.3\\ \Rightarrow A=-2.4\end{array}$

Percent of change $=\frac{-2.4}{48.3}\times 100$

  $\Rightarrow$ Percent of change $=\frac{-240}{48.3}$

  $\Rightarrow$ Percent of change $=-4.968$

Therefore,

Percent of change is $4.968\%$ from budget in $2010$ to budget in $2011$ and negative sign indicates percent of decrease.

From given information

Budget in $2011$

  $=45.9$ millions of $.

Budget in $2012$

  $=55.1$ millions of $.

Amount of change $=$ Budget in $2012$

  $-$ Budget in $2011$

  $\begin{array}{l}\Rightarrow A=55.1-45.9\\ \Rightarrow A=9.2\end{array}$

Percent of change $=\frac{9.2}{45.9}\times 100$

  $\Rightarrow$ Percent of change $=\frac{920}{45.9}$

  $\Rightarrow$ Percent of change $=20.04$

Therefore,

Percent of change is $20.04\%$ from budget in $2011$ to budget in $2012$ and positive sign indicates percent of increase.

Therefore

On comparing all percent of changes from $2009$ to $2012$

We can say that

Option C is correct as

Percent of change was $20\%$ from budget $2011$ to budget in $2012$ .

The budget increased $20\%$ from $2011$ to $2012$