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Chapter 1: Problem 12

The percent increase from 5 to 12 is equal to th percent increase from 12 to what number? $$ \begin{array}{l}{\text { (A) } 16.8} \\ {\text { (B) } 19.0} \\ {\text { (C) } 26.6} \\ {\text { (D) } 28.8}\end{array} $$

Short Answer

Expert verified
(D) 28.8

Step by step solution

01

- Understand Percent Increase Formula

The percent increase from a number a to a number b is calculated by the formula: \ \[ \text{Percent Increase} = \frac{b - a}{a} \times 100 \% \]
02

- Calculate Percent Increase from 5 to 12

Using the formula: \ \[ \text{Percent Increase} = \frac{12 - 5}{5} \times 100 \% = \frac{7}{5} \times 100 \% = 140 \% \] So, the percent increase from 5 to 12 is 140%.
03

- Set up Equation for Second Percent Increase

We are given that the same percent increase (140%) from 12 leads to another number x. We set up the equation: \ \[ 140 \% = \frac{x - 12}{12} \times 100 \% \]
04

- Solve for x

Rearrange the equation to solve for x: \ \[ 140 \% = \frac{x - 12}{12} \times 100 \% \] \ \[ 1.40 = \frac{x - 12}{12} \] \ \[ 1.40 \times 12 = x - 12 \] \ \[ 16.8 = x - 12 \] \ Adding 12 to both sides gives: \ \[ x = 16.8 + 12 = 28.8 \]
05

- Verify the Result

We find that the number that satisfies the condition is 28.8. The value 28.8 matches option D.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

percent increase formula
The percent increase formula is a fundamental tool for measuring growth between two values. When you want to determine the percent increase from an initial value, say 'a', to a new value, 'b', use the following formula:
\[ \text{Percent Increase} = \frac{b - a}{a} \times 100 \,\text{\textpercent} \]
In this equation, 'a' represents the original number, 'b' represents the new number, and the result tells you the percentage increase. This formula is widely used not only in academic settings like the SAT but also in real-life scenarios such as business and finance.
mathematical equations
Mathematical equations help us express relationships and solve problems efficiently. In the context of percent increase, an equation helps in transitioning from one value to another.
When you are given the percentage increase and need to find an unknown quantity, set up the equation based on the percent increase formula. For instance:
Suppose you know a 140% increase from 12 leads to another number 'x'. Set up the equation as:
\[ 140\text{\textpercent} = \frac{x - 12}{12} \times 100\text{\textpercent} \]
This kind of equation ensures that you can solve for 'x' effectively.
problem-solving steps
Solving percent increase problems involves several logical steps. Here's a step-by-step breakdown to solve the given exercise:
1. **Understand the given data**: Know your initial and final values. Here you need to find the number that gives a 140% increase from 12.
2. **Apply the percent increase formula**: Use the formula to find the increase percentage.
3. **Set up the equation**: Given the percent increase is the same (140%), set up the equation \[ 140\text{\textpercent} = \frac{x - 12}{12} \times 100\text{\textpercent}\]
4. **Solve for the unknown**: Rearrange the formula to isolate 'x'. Multiply both sides of the equation to solve for 'x'.
5. **Verify your result**: Always substitute back into the context to ensure the solution is correct.
SAT math
Understanding concepts like percent increase is crucial for SAT math success. The SAT frequently features problems requiring percent-based calculations. Practicing problems like the one given helps in:
* Grasping fundamental formulas.
* Enhancing problem-solving skills by setting up and solving equations.
* Improving your ability to approach questions logically.
By mastering such exercises, you're not only preparing for exams but also developing critical thinking applicable in various real-world situations.

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Most popular questions from this chapter

Rory left home and drove straight to the airport at an average speed of 45 miles per hour. He returned home along the same route, but traffic slowed him down and he only averaged 30 miles per hour on the return trip. If his total travel time was 2 hours and 30 minutes, how far is it, in miles, from Rory's house to the airport?

A microbiologist is studying the effects of a new antibiotic on a culture of \(20,000\) bacteria. When the antibiotic is added to the culture, the number of bacteria is reduced by half every hour. What kind of function best models the number of bacteria remaining in the culture after the antibiotic is added? $$\begin{array}{l}{\text { (A) A linear function }} \\ {\text { (B) A quadratic function }} \\ {\text { (C) A polynomial function }} \\ {\text { (D) An exponential function }}\end{array}$$

An electrician charges a one-time site visit fee to evaluate a potential job. If the electrician accepts the job, he charges an hourly rate plus the cost of any materials needed to complete the job. The electrician also charges for tax, but only on the cost of the materials. If the total cost of completing a job that takes \(h\) hours is given by the function \(C(h)=45 h+\) \(1.06(82.5)+75,\) then the term 1.06\((82.5)\) represents $$ \begin{array}{l}{\text { (A) the hourly rate. }} \\ {\text { (B) the site visit fee. }} \\ {\text { (C) the cost of the materials, including tax. }} \\\ {\text { (D) the cost of the materials, not including tax. }}\end{array} $$

Carbon makes up what percent of the mass of one mole of chloroform? Round your answer to the nearest whole percent and ignore the percent sign when entering your answer.

Some doctors base the dosage of a drug to be given to a patient on the patient's body surface area \((B S A) .\) The most commonly used formula for calculating \(B S A\) is \(B S A=\sqrt{\frac{w h}{3,600}},\) where \(w\) is the patient's weight \((\mathrm{in}\) \(\mathrm{kg} ), h\) is the patient's height (in \(\mathrm{cm} ),\) and \(B S A\) is measured in square meters. How tall \((\mathrm{in} \mathrm{cm})\) is a patient who weighs 150 \(\mathrm{kg}\) and has a \(B S A\) of 2\(\sqrt{2} \mathrm{m}^{2}\) ?
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