Chapter 2

The sum of \(\frac{2}{3}\) and four times a number is equal to \(\frac{5}{6}\) subtracted from five times the number. Find the number.

Solve each inequality. Write each answer using solution set notation. $$ 4-x<8 x+2 x $$

Solve. See Examples 1 through 7 $$ \frac{5(x-1)}{4}=\frac{3(x+1)}{2} $$

By doubling each dimension, the area of a triangle increased from 6 square miles to 24 square miles. Find the percent increase in area.

Solve. $$ 15 x+20-10 x-9=25 x+8-21 x-7 $$

Solve each equation. See Examples 9 and \(10 .\) \(\frac{1}{3}(3 x-1)=-\frac{1}{10}-\frac{2}{10}\)

Hertz Car Rental charges a daily rate of \(\$ 39\) plus \(\$ 0.20\) per mile for a certain car. Suppose that you rent that car for a day and your bill (before taxes) is \(\$ 95\). How many miles did you drive?

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

Solve. See Examples 1 through 7 $$ 0.7 x-2.3=0.5 $$

A gasoline station recently increased the price of one grade of gasoline by \(5 \% .\) If this gasoline originally cost \(\$ 2.20\) per gallon, find the mark-up and the new price.

Solve. $$ 7(6+w)=6(2+w) $$

Solve each equation. See Examples 9 and \(10 .\) \(-10 z-0.5=-20 z+1.6\)

A woman's \(\$ 15,000\) estate is to be divided so that her husband receives twice as much as her son. Find the amount of money that her husband receives and the amount of money that her son receives.

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

Solve. See Examples 1 through 7 $$ 0.9 x-4.1=0.4 $$

The price of a biology book recently increased by \(10 \%\). If this book originally cost \(\$ 89.90,\) find the mark-up and the new price.

Solve. $$ 6(5+c)=5(c-4) $$

Solve each equation. See Examples 9 and \(10 .\) \(-14 y-1.8=-24 y+3.9\)

During the 2009 Rose Bowl, University of Southern California beat Pennsylvania State University by 14 points. If their combined scores totaled \(62,\) find the individual team scores.

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

How much of an alloy that is \(20 \%\) copper should be mixed with 200 ounces of an alloy that is \(50 \%\) copper in order to get an alloy that is \(30 \%\) copper?

Solve. $$ n+4=3.6 $$

Solve each equation. See Examples 9 and \(10 .\) \(-4 x+20=4 x-20\)

Piranha fish require 1.5 cubic feet of water per fish to maintain a healthy environment. Find the maximum number of piranhas you could put in a tank measuring 8 feet by 3 feet by 6 feet.

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

Solve. See Examples 1 through 7 $$ 3(2 x-1)+5=6 x+2 $$

How much water should be added to 30 gallons of a solution that is \(70 \%\) antifreeze in order to get a mixture that is \(60 \%\) antifreeze?

Solve. $$ m+2=7.1 $$

Find the maximum number of goldfish you can put in a cylindrical tank whose diameter is 8 meters and whose height is 3 meters, if each goldfish needs 2 cubic meters of water. \(\left(V=\pi r^{2} h\right)\)

The number of counties in California and the number of counties in Montana are consecutive even integers whose sum is 114 . If California has more counties than Montana, how many counties does each state have? (Source: The World Almanac and Book of Facts)

Solve each inequality. Write each answer using solution set notation. $$ 4(3 x-1) \leq 5(2 x-4) $$

Solve. See Examples 1 through 7 $$ 4(2 n+1)=3(6 n+3)+1 $$

During the \(1982-1983\) term, the Supreme Court made 151 decisions while during the \(2007-2008\) term, they only made 72 . Find the percent decrease in number of decisions. Round to the nearest tenth of a percent.

Solve. $$ 10-(2 x-4)=7-3 x $$

\(42=7 x\)

A lawn is in the shape of a trapezoid with a height of 60 feet and bases of 70 feet and 130 feet. How many bags of fertilizer must be purchased to cover the lawn if each bag covers 4000 square feet? \(\left(A=\frac{1}{2} h(B+b)\right)\)

A student is building a bookcase with stepped shelves for her dorm room. She buys a 48 -inch board and wants to cut the board into three pieces with lengths equal to three consecutive even integers. Find the three board lengths.

Solve each inequality. Write each answer using solution set notation. $$ 3(5 x-4) \leq 4(3 x-2) $$

The number of farms in the United States is decreasing. In \(1940,\) there were approximately 6.3 million farms, while in 2007 there were only 2.1 million farms. Find the percent decrease in the number of farms. Round to the nearest tenth of a percent.

Solve. $$ 15-(6-7 k)=2+6 k $$

\(81=3 x\)

If the area of a right-triangularly shaped sail is 20 square feet and its base is 5 feet, find the height of the sail. \(\left(A=\frac{1}{2} b h\right)\)

Over the past few years the satellite Voyager II has passed by the planets Saturn, Uranus, and Neptune, continually updating information about these planets, including the number of moons for each. Uranus is now believed to have 13 more moons than Neptune. Also, Saturn is now believed to have 2 more than twice the number of moons of Neptune. If the total number of moons for these planets is 47 , find the number of moons for each planet. (Source: National Space Science Data Center)

Solve each inequality. Write each answer using solution set notation. $$ 3(x+2)-6>-2(x-3)+14 $$

A company recently downsized its number of employees by \(35 \%\). If there are still 78 employees, how many employees were there prior to the layoffs?

Solve. $$ \frac{1}{3}=x+\frac{2}{3} $$

\(4.4=-0.8 x\)

Maria's Pizza sells one 16 -inch cheese pizza or two 10 -inch cheese pizzas for \(\$ 9.99 .\) Determine which size gives more pizza. \(\left(A=\pi r^{2}\right)\)

The Mars Odyssey spacecraft was launched in 2001 , beginning a multiyear mission to observe and map the planet Mars. Mars Odyssey was launched on Boeing's Delta II 7925 launch vehicle using nine strap-on solid rocket motors. Each solid rocket motor has a height that is 8 meters more than 5 times its diameter. If the sum of the height and the diameter for a single solid rocket motor is 14 meters, find each dimension. (Recently, NASA approved a continuation of the Odyssey mission through September 2010.) (Source: NASA)

Solve each inequality. Write each answer using solution set notation. $$ 7(x-2)+x \leq-4(5-x)-12 $$