4.2: Applications Involving Percentages
- Page ID
- 139270
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)
( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\id}{\mathrm{id}}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\kernel}{\mathrm{null}\,}\)
\( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\)
\( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\)
\( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)
\( \newcommand{\vectorA}[1]{\vec{#1}} % arrow\)
\( \newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow\)
\( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vectorC}[1]{\textbf{#1}} \)
\( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)
\( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)
\( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
If we have a part that is some percent of a whole, then percent \(=\dfrac{\text { part }}{\text { whole }}\), or equivalently, part \(=\) percent \(\cdot\) whole To do the calculations, we write the percent as a decimal.
243 people out of 400 state that they like dogs. What percent is this?
Solution
\( \dfrac{243}{400}=0.6075=\dfrac{60.75}{100} \). This is 60.75 % .
Notice that the percent can be found from the equivalent decimal by moving the decimal point two places to the right
To win the election as president of the United States of America, a person must obtain 270 out of 538 possible votes from the electoral college. What percentage of the overall electoral votes is this? Round your answer to the nearest tenth of a percent.
- Answer
-
50.2%
The sales tax in a town is 9.4%. How much tax will you pay on a $140 purchase?
Solution
Here, $140 is the whole, and we want to find 9.4% of $140. We start by writing the percent as a decimal by moving the decimal point two places to the left (which is equivalent to dividing by 100). We can then compute: Tax = 0.094(140) = $13.16
In a recent poll, 28% of the 750 individuals polled indicated that they would vote purely Democratic in the next election. How many of the individuals would vote a straight Democratic ticket?
- Answer
-
210
A lender requires a minimum down payment of 12% of the value of the home. You have $22,020 cash available to use as a down payment toward a home. Determine the maximum home value that you can finance.
Solution
To compute the maximum home value, we need to understand what the $22,020 represents. This is the down payment; we need to find the value of the home. In this case, the down payment is the “part” and the home value is the “whole.” Recall that part = percent x whole
Let V represent the value of the home. Since we know that the down payment is 12% of the value of the home, we can write the equation: 22,020 = 0.12V.
Solving this equation for V, we get V= \(\dfrac{22,020}{0.12}=183,500 \)
So, with $22,020 cash available to use as a down payment, you can afford to finance a home worth at most $183,500.
One banana contains about 425mg of potassium. That is about 13% of the recommended daily amount of potassium. How much potassium should be consumed daily?
- Answer
-
3,269mg, or 3.269 g
When working with percentages, it is very important to understand the quantities being compared. Consider the examples below.
In the 2004 vice-presidential debates, Edwards's claimed that US forces have suffered "90% of the coalition casualties" in Iraq. Cheney disputed this, saying that in fact Iraqi security forces and coalition allies "have taken almost 50 percent" of the casualties. Who is correct?
Solution
Without more information, it is hard for us to judge who is correct, but we can easily conclude that these two percentages are talking about different things, so one does not necessarily contradict the other. Edward’s claim was a percent of coalition forces, while Cheney’s claim was a percent with both coalition and Iraqi security forces. It turns out both statistics are in fact fairly accurate.
Over the basketball season, Isaac scores on 40% of 2-point field goal attempts, and on 30% of 3-point of field goal attempts. Find Isaac’s overall field goal percentage.
Solution
It is very tempting to average these values, and claim the overall average is 35%, but this is likely not correct, since most players make many more 2-point attempts than 3-point attempts. We don’t actually have enough information to answer the question. Suppose Isaac attempted 200 2-point field goals and 100 3-point field goals. Then he made 200(0.40) = 80 2-point shots and 100(0.30) = 30 3-point shots. Overall, Isaac made 110shots out of 300, for a \(\dfrac{110}{300}=0.367=36.7\) overall field goal percentage.