Chapter 2

Solve. See Examples 1 through 7 $$ \frac{7}{8} x+\frac{1}{4}=\frac{3}{4} x $$

The average number of children born to each U.S. woman has decreased by \(44 \%\) since 1920 . If this average is now \(1.9,\) find the average in \(1920 .\) Round to the nearest tenth.

Solve. $$ \frac{1}{11}=y+\frac{10}{11} $$

\(6.3=-0.6 x\)

Find how much rope is needed to wrap around Earth at the equator, if the radius of Earth is 4000 miles.

If the sum of a number and five is tripled, the result is one less than twice the number. Find the number.

Solve each inequality. Write each answer using solution set notation. $$ -5(1-x)+x \leq-(6-2 x)+6 $$

Solve. See Examples 1 through 7 $$ \frac{x}{2}-1=\frac{x}{5}+2 $$

Nordstrom advertised a \(25 \%\) -off sale. If a London Fog coat originally sold for \(\$ 256,\) find the decrease in price and the sale price.

Solve. $$ -6.5-4 x-1.6-3 x=-6 x+9.8 $$

\(6 x+10=-20\)

A Japanese "bullet" train set a new world record for train speed at 552 kilometers per hour during a manned test run on the Yamanashi Maglev Test Line in April 1999. The Yamanashi Maglev Test Line is 42.8 kilometers long. How many minutes would a test run on the Yamanashi Line last at this record- setting speed? Round to the nearest hundredth of a minute.

Twice the sum of a number and six equals three times the sum of the number and four. Find the number.

Solve each inequality. Write each answer using solution set notation. $$ -2(x-4)-3 x<-(4 x+1)+2 x $$

Solve. See Examples 1 through 7 $$ \frac{x}{5}-7=\frac{x}{3}-5 $$

A gasoline station decreased the price of a \(\$ 0.95\) cola by \(15 \%\). Find the decrease in price and the new price.

Solve. $$ -1.4-7 x-3.6-2 x=-8 x+4.4 $$

\(10 y+15=-5\)

In \(1983,\) the Hawaiian volcano Kilauea began erupting in a series of episodes still occurring at the time of this writing. At times, the lava flows advanced at speeds of up to 0.5 kilometer per hour. In 1983 and 1984 lava flows destroyed 16 homes in the Royal Gardens subdivision, about \(6 \mathrm{~km}\) away from the eruption site. Roughly how long did it take the lava to reach Royal Gardens?

The area of the Sahara Desert is 7 times the area of the Gobi Desert. If the sum of their areas is 4,000,000 square miles, find the area of each desert.

Solve each inequality. Write each answer using solution set notation. $$ \frac{1}{4}(x+4)<\frac{1}{5}(2 x+3) $$

Solve. See Examples 1 through 7 $$ 2(x+3)-5=5 x-3(1+x) $$

Scoville units are used to measure the hotness of a pepper. Measuring 577 thousand Scoville units, the "Red Savina" habañero pepper was known as the hottest chili pepper. That has recently changed with the discovery of Naga Jolokia pepper from India. It measures \(48 \%\) hotter than the habañero. Find the measure of the Naga Jolokia pepper. Round to the nearest thousand units.

Write each algebraic expression described. A 10 -foot board is cut into two pieces. If one piece is \(x\) feet long, express the other length in terms of \(x\).

\(5-0.3 k=5\)

The perimeter of an equilateral triangle is 7 inches more than the perimeter of a square, and the side of the triangle is 5 inches longer than the side of the square. Find the side of the triangle.

The largest meteorite in the world is the Hoba West, located in Namibia. Its weight is 3 times the weight of the Armanty meteorite, located in Outer Mongolia. If the sum of their weights is 88 tons, find the weight of each.

Solve each inequality. Write each answer using solution set notation. $$ \frac{1}{2}(x-5)<\frac{1}{3}(2 x-1) $$

Solve. See Examples 1 through 7 $$ 4(2+x)+1=7 x-3(x-2) $$

As of this writing, the women's record for throwing a disc (like a heavy Frisbee) was set by Valarie Jenkins of the United States in 2008. Her throw was 148.00 meters. The men's world record was set by Christian Sandstrom of Sweden in 2002 . His throw was \(68.9 \%\) farther than Valarie's. Find the distance of his throw. Round to the nearest meter. (Source: World Flying Disc Federation)

Write each algebraic expression described. A 5 -foot piece of string is cut into two pieces. If one piece is \(x\) feet long, express the other length in terms of \(x\).

\(2-0.4 p=2\)

A square animal pen and a pen shaped like an equilateral triangle have equal perimeters. Find the length of the sides of each pen if the sides of the triangular pen are fifteen less than twice a side of the square pen.

In the 2008 Summer Olympics, Korea won more gold medals than Germany, which won more gold medals than Australia. If the numbers of gold medals won by these three countries are three consecutive integers whose sum is \(21,\) find the number of gold medals won by each. (Source: Beijing 2008 Olympics)

Solve each inequality. Write each answer using solution set notation. $$ -5 x+4 \leq-4(x-1) $$

Solve. See Examples 1 through 7 $$ 0.06-0.01(x+1)=-0.02(2-x) $$

A recent survey showed that \(42 \%\) of recent college graduates named flexible hours as their most desired employment benefit. In a graduating class of 860 college students, how many would you expect to rank flexible hours as their top priority in job benefits? (Round to the nearest whole.) (Source: JobTrak.com)

Write each algebraic expression described. Recall that two angles are supplementary if their sum is \(180^{\circ} .\) If one angle measures \(x^{\circ},\) express the measure of its supplement in terms of \(x\).

\(13 x-5=11 x-11\)

Find how long it takes Tran Nguyen to drive 135 miles on I-10 if he merges onto I-10 at 10 a.m. and drives nonstop with his cruise control set on \(60 \mathrm{mph} .\)

To make an international telephone call, you need the code for the country you are calling. The codes for Mali Republic, Côte d'Ivoire, and Niger are three consecutive odd integers whose sum is \(675 .\) Find the code for each country.

Solve each inequality. Write each answer using solution set notation. $$ -6 x+2<-3(x+4) $$

A recent survey showed that \(64 \%\) of U.S. colleges have Internet access in their classrooms. There are approximately 9800 post-secondary institutions in the United States. How many of these would you expect to have Internet access in their classrooms? (Source: Market Data Retrieval, National Center for Education Statistics)

Write each algebraic expression described. Recall that two angles are complementary if their sum is \(90^{\circ} .\) If one angle measures \(x^{\circ},\) express the measure of its complement in terms of \(x\).

\(20 x-20=16 x-40\)

Beaumont, Texas, is about 150 miles from Toledo Bend. If Leo Miller leaves Beaumont at 4 a.m. and averages \(45 \mathrm{mph}\), when should he arrive at Toledo Bend?

In a runoff election in Georgia for a seat in the U.S. Senate, incumbent Senator Saxby Chambliss received 315,217 more votes than challenger Jim Martin. If the total number of votes cast was \(2,126,491,\) find the number of votes for each candidate. (Source: New York Times)

Six more than twice a number is greater than negative fourteen. Find all numbers that make this statement true.

Solve. See Examples 1 through 7 $$ \frac{9}{2}+\frac{5}{2} y=2 y-4 $$

A new self-tanning lotion for everyday use is to be sold. First, an experimental lotion mixture is made by mixing 800 ounces of everyday moisturizing lotion worth \(\$ 0.30\) an ounce with self-tanning lotion worth \(\$ 3\) per ounce. If the experimental lotion is to cost \(\$ 1.20\) per ounce, how many ounces of the selftanning lotion should be in the mixture?