Chapter 1

The formula \(P=\left(\frac{w}{w+i}\right) 100\) represents the relationship of the percent of X-rays absorbed by an antiscatter grid \(P\), the width of each grid strip \(w\), and the width between the grid strips \(i\). If the width of each grid strip is 50 micrometers and the width between the grid strips is 350 micrometers, find the percent of X-rays absorbed. Round to the nearest percent.

The regular price of a portable GPS vehicle navigator is \(\$ 499.99\). The sale price is \(\$ 389.99\). Find the percent discount. Round to the nearest percent.

Problem: Complete the "Make a plan" step for this problem: The Government Accountability Office found cost overruns totaling \(\$ 295\) billion in 95 major government defense projects. Find the average amount of overrun per project. Round to the nearest tenth of a billion. Incorrect Answer: The average amount is the product of the overruns and the number of projects. A word equation is average amount \(=\) (cost overruns) (number of projects).

\(\left(\frac{2}{3}+\frac{1}{2}\right)^{2}\)

The intensity of \(\mathrm{X}\)-ray radiation depends on the distance from the source of radiation. If the distance from the source of radiation changes from \(D_{1}\) to \(D_{2}\), the intensity changes from intensity \(I_{1}\) to \(I_{2}\). The formula for finding the new intensity is \(I_{2}=\frac{I_{1} \cdot\left(D_{1}\right)^{2}}{\left(D_{2}\right)^{2}}\). When \(D_{1}\) is \(25 \mathrm{~m}\), the intensity \(I_{1}\) is 620 roentgen per hour. Find the intensity of radiation \(I_{2}\) if \(D_{2}\) is \(5 \mathrm{~m}\).

The regular price of a camp axe with a sheath is \(\$ 62.00\). The sale price is \(\$ 30.52\). Find the percent discount. Round to the nearest percent.

\(18\left(\frac{5}{6} h-\frac{1}{3}\right)-7\)

\(\left(\frac{3}{4}+\frac{1}{2}\right)^{2}\)

A furniture store bought a recliner from a wholesaler for \(\$ 150\). It then sold the recliner for \(\$ 499\). Find the percent markup. Round to the nearest percent.

Problem: Complete the "Understand the problem," "Make a plan," and "Carry out the plan" steps for this problem: Find the percent of community college students nationwide who can attend college full-time. If students can attend full-time, they are four times as likely to complete as part-timers. But only 29 percent of California students can attend full-time. That's 12 percentage points below the national community college figure. (Source; www .communitycollegetimes.com, Aug. 3, 2007)

\(\frac{1}{2}(6 c+9)-\frac{3}{4}(8 c-11)\)

\(\frac{1}{8} \div \frac{1}{2}-\frac{3}{4}\)

A bookstore bought a used book from a student for \(\$ 20\). It then resold the book as a used book for \(\$ 85\). Find the percent markup.

\(\frac{1}{10} \div \frac{1}{5}-\frac{3}{5}\)

An employee works for 8 hours at \(\$ 9.25\) per hour. The employer withholds \(7.65 \%\) of his gross wages for Social Security and Medicare taxes. Find the amount of wages after with holding.

Find \(15 \%\) of \(6 .\)

\(\frac{2}{5}(8 z-6)+\frac{3}{7}(2 z+15)\)

\(3-4 \cdot 2+9\)

An employee works for 8 hours at \(\$ 9.75\) per hour. The employer withholds \(7.65 \%\) of her gross wages for Social Security and Medicare taxes. Find the amount of wages after with holding.

\(\frac{3}{8}(15 z-7)+\frac{2}{9}(3 z+20)\)

\(5-4 \cdot 3+8\)

If the market value per share of Microsoft Corp. stock is \(\$ 30.16\) and the earnings per share are \(\$ 1.39\), find the \(\mathrm{P} / \mathrm{E}\) ratio. Round to the nearest hundredth.

What percent is \(\$ 5\) of \(\$ 80\) ?

Explain why \(6 x\) and \(5 y\) are not like terms.

\(-15-(3-8)\)

If the market value per share of Apple, Inc. stock is \(\$ 138.91\) and the earnings per share is \(\$ 3.16\), find the \(\mathrm{P} / \mathrm{E}\) ratio. Round to the nearest hundredth.

Problem: Complete the "Understand the problem," "Make a plan," and "Complete the plan" steps. A 20 -acre field is going to be divided into building lots. The area of each lot is \(\frac{2}{5}\) acre. Find the number of lots in the development. Incorrect Answer: The unknown is the number of lots: \(L\) = number of lots. To find the number of lots, multiply the area by the number of lots. $$ \begin{aligned} &L=\left(\frac{2}{5}\right)(20) \\ &L=8 \text { lots } \end{aligned} $$

Rewrite \(0.97\) as a percent.

Explain why \(9 a\) and \(3 b\) are not like terms.

\(-21-(4-9)\)

Clark's rule is "Multiply the adult dose with the weight of the child (in pounds) and divide by 150 (the average weight of an adult)." Assign the variables and write a formula that describes Clark's rule.

Explain why \(2 x^{2} y\) and \(8 x y^{2}\) are not like terms.

\(\frac{14-2}{6-3}\)

Fried's rule for infants is "Divide the age in months by 150 and multiply it by the adult dose." Assign the variables and write a formula that describes Fried's rule.

Problem: Complete the "Understand the problem," "Make a plan," and "Complete the plan" steps. The regular price of a 12 -cup programmable coffee maker is \(\$ 79.99\). The sale price is \(\$ 59.99\). Find the percent discount. Round to the nearest percent. Incorrect Answer: The unknown is the percent discount; \(P=\) percent discount. A word equation is percent decrease \(=\left(\frac{\text { decrease in price }}{\text { sale price }}\right)(100) \%\). $$ \begin{aligned} &P=\left(\frac{\$ 79.99-\$ 59.99}{\$ 59.99}\right)(100) \% \\ &P=33 \% \text { decrease } \end{aligned} $$

Explain why \(7 a^{2} b\) and \(5 a b^{2}\) are not like terms.

\(\frac{15-3}{2+4}\)

\(5^{2}\)

A student said that the expression \((5 x)(3 y)\) cannot be simplified because \(5 x\) and \(3 y\) are not like terms. Explain why the student is wrong.

\(\frac{14-2^{2}}{6+4}\)

\(2^{3}\)

A student said that the expression \((2 a)(9 b)\) cannot be simplified because \(2 a\) and \(9 b\) are not like terms. Explain why the student is wrong.

\(\frac{15-3^{2}}{2+4}\)

\((-2)^{3}\)

\(12+4^{2} \cdot 3 \div 2+4\)

\((-5)^{2}\)

To add \(\frac{5}{6} x\) and \(\frac{1}{4} x\), the fractions can be rewritten with the common denominator 24 , or they can be rewritten with the least common denominator, 12. Explain the advantage of using the least common denominator.

\(15+6^{2} \cdot 2 \div 3+9\)

If you use e-mail to communicate with your instructor, your instructor may prefer that you present the information more formally than you would if you were text messaging or using social media such as Twitter. Write an e-mail to your instructor that explains that you are too ill to come to class for a test. Ask what you should do about missing the exam. If your college does not have guidelines for writing e-mail, use the format shown below. To: (Instructor e-mail address) Subject: (include the name of your class and section number or class time) Salutation: (use the title and name preferred by your instructor) Body: (write in complete standard English sentences; check your spelling. Do not use smiley faces, other emoticons, or inappropriate language.) Signature: (use your full name)

Problem: Simplify: \(10-6(x-3)\) Incorrect Answer: \(10-6(x-3)\) $$ \begin{aligned} &=4(x-3) \\ &=4 x-12 \end{aligned} $$