Chapter 4

Solve each of the equations. $$0.09 x=550-0.11(5400-x)$$

Solve each of the equations. $$\frac{n+1}{n}=\frac{8}{7}$$

A tank contains 50 gallons of a \(40 \%\) solution of antifreeze. How much solution needs to be drained out and replaced with pure antifreeze to obtain a \(50 \%\) solution?

The width of a rectangle is 1 foot more than one-third of its length. If the perimeter of the rectangle is 74 feet, find the area of the rectangle.

For Problems 11-32, use the geometric formulas given in this section to help solve the problems. (Objective 3 ) Find the area of a circular plot of ground that has a radius of length 14 meters. Use \(3 \frac{1}{7}\) as an approximation for \(\pi\).

Solve each of the equations. $$0.08 x=580-0.1(6000-x)$$

Solve each of the equations. $$\frac{5}{6}=\frac{n}{n+1}$$

How many gallons of a \(15 \%\) salt solution must be mixed with 8 gallons of a \(20 \%\) salt solution to obtain a \(17 \%\) salt solution?

The perimeter of a triangle is 100 feet. The longest side is 3 feet less than twice the shortest side, and the third side is 7 feet longer than the shortest side. Find the lengths of the sides of the triangle.

For Problems 11-32, use the geometric formulas given in this section to help solve the problems. (Objective 3 ) Find the area of a circular region that has a diameter of 1 yard. Express the answer in terms of \(\pi\).

Set up an equation and solve each problem. (Objectives 2 and 3) Tom bought an electric drill at a \(30 \%\) discount sale for \$35. What was the original price of the drill?

Solve each of the equations. $$\frac{x-1}{2}-1=\frac{3}{4}$$

How many liters of a \(10 \%\) salt solution must be mixed with 15 liters of a \(40 \%\) salt solution to obtain a \(20 \%\) salt solution?

A triangular plot of ground has a perimeter of 54 yards. The longest side is twice the shortest side, and the third side is 2 yards longer than the shortest side. Find the lengths of the sides of the triangle.

For Problems 11-32, use the geometric formulas given in this section to help solve the problems. (Objective 3 ) Find the area of a circular region if the circumference is \(12 \pi\) units. Express the answer in terms of \(\pi\).

Set up an equation and solve each problem. (Objectives 2 and 3) Magda bought a dress for \(\$ 140\), which represents a \(20 \%\) E discount of the original price. What was the original price of the dress?

Solve each of the equations. $$-2+\frac{x+3}{4}=\frac{5}{6}$$

Thirty ounces of a punch that contains \(10 \%\) grapefruit juice is added to 50 ounces of a punch that contains \(20 \%\) grapefruit juice. Find the percent of grapefruit juice in the resulting mixture.

The second side of a triangle is 1 centimeter longer than three times the first side. The third side is 2 centimeters longer than the second side. If the perimeter is 46 centimeters, find the length of each side of the triangle.

For Problems 11-32, use the geometric formulas given in this section to help solve the problems. (Objective 3 ) Find the total surface area and volume of a sphere that has a radius 9 inches long. Express the answers in terms of \(\pi\).

Set up an equation and solve each problem. (Objectives 2 and 3) Find the cost of a \(\$ 4800\) wide-screen high-definition television that is on sale for \(25 \%\) off.

Solve each of the equations. $$-3-\frac{x+4}{5}=\frac{3}{2}$$

Suppose that 20 gallons of a \(20 \%\) salt solution is mixed with 30 gallons of a \(25 \%\) salt solution. What is the percent of salt in the resulting solution?

The second side of a triangle is 3 meters shorter than twice the first side. The third side is 4 meters longer than the second side. If the perimeter is 58 meters, find the length of each side of the triangle.

For Problems 11-32, use the geometric formulas given in this section to help solve the problems. (Objective 3 ) A circular pool is 34 feet in diameter and has a flagstone walk around it that is 3 feet wide (see Figure 4.19). Find the area of the walk. Express the answer in terms of \(\pi\).

Set up an equation and solve each problem. (Objectives 2 and 3) Byron purchased a computer monitor at a \(10 \%\) discount sale for \(\$ 121.50\). What was the original price of the monitor?

Solve each of the equations. $$\frac{x-5}{3}+2=\frac{5}{9}$$

Suppose that the perimeter of a square equals the perimeter of a rectangle. The width of the rectangle is 9 inches less than twice the side of the square, and the length of the rectangle is 3 inches less than twice the side of the square. Find the dimensions of the square and the rectangle.

The perimeter of an equilateral triangle is 4 centimeters more than the perimeter of a square, and the length of a side of the triangle is 4 centimeters more than the length of a side of the square. Find the length of a side of the equilateral triangle. (An equilateral triangle has three sides of the same length.)

For Problems 11-32, use the geometric formulas given in this section to help solve the problems. (Objective 3 ) Find the volume and total surface area of a right circular cylinder that has a radius of 8 feet and a height of 18 feet. Express the answers in terms of \(\pi\).

Set up an equation and solve each problem. (Objectives 2 and 3) Suppose that Jack bought a \(\$ 32\) putter on sale for \(35 \%\) off. How much did he pay for the putter?

Solve each of the equations. $$\frac{n}{150-n}=\frac{1}{2}$$

The perimeter of a triangle is 40 centimeters. The longest side is 1 centimeter longer than twice the shortest side. The other side is 2 centimeters shorter than the longest side. Find the lengths of the three sides.

Suppose that a square and an equilateral triangle have the same perimeter. Each side of the equilateral triangle is 6 centimeters longer than each side of the square. Find the length of each side of the square. (An equilateral triangle has three sides of the same length.)

For Problems 11-32, use the geometric formulas given in this section to help solve the problems. (Objective 3 ) Find the total surface area and volume of a sphere that has a diameter 12 centimeters long. Express the answers in terms of \(\pi\).

Set up an equation and solve each problem. (Objectives 2 and 3) Swati bought a 13 -inch portable color TV for \(20 \%\) off of the list price. The list price was \(\$ 229.95\). What did she pay for the TV?

Solve each of the equations. $$\frac{n}{200-n}=\frac{3}{5}$$

Andy starts walking from point A at 2 miles per hour. One-half hour later, Aaron starts walking from point A at \(3 \frac{1}{2}\) miles per hour and follows the same route. How long will it take Aaron to catch up with Andy?

Suppose that the length of a radius of a circle is the same as the length of a side of a square. If the circumference of the circle is \(15.96\) centimeters longer than the perimeter of the square, find the length of a radius of the circle. (Use \(3.14\) as an approximation for \(\pi\).)

For Problems 11-32, use the geometric formulas given in this section to help solve the problems. (Objective 3 ) If the volume of a right circular cone is \(324 \pi\) cubic inches, and a radius of the base is 9 inches long, find the height of the cone.

Set up an equation and solve each problem. (Objectives 2 and 3) Pierre bought a coat for \(\$ 126\) that was listed for \(\$ 180\). What rate of discount did he receive?

Solve each of the equations. $$\frac{300-n}{n}=\frac{3}{2}$$

Suppose that Karen, riding her bicycle at 15 miles per hour, rode 10 miles farther than Michelle, who was riding her bicycle at 14 miles per hour. Karen rode for 30 minutes longer than Michelle. How long did Michelle and Karen each ride their bicycles?

The circumference of a circle is \(2.24\) centimeters more than six times the length of a radius. Find the radius of the circle. (Use \(3.14\) as an approximation for \(\pi\).)

For Problems 11-32, use the geometric formulas given in this section to help solve the problems. (Objective 3 ) Find the volume and total surface area of a tin can if the radius of the base is 3 centimeters, and the height of the can is 10 centimeters. Express the answers in terms of \(\pi\).

Set up an equation and solve each problem. (Objectives 2 and 3) Phoebe paid \(\$ 32\) for a pair of sandals that was listed for S40. What rate of discount did she receive?

Solve each of the equations. $$\frac{80-n}{n}=\frac{7}{9}$$

Pam is half as old as her brother Bill. Six years ago Bill was four times older than Pam. How old is each sibling now? (See Problems 40-42 in Appendix B for more "age" problems.)

Sandy leaves a town traveling in her car at a rate of 45 miles per hour. One hour later, Monica leaves the same town traveling the same route at a rate of 50 miles per hour. How long will it take Monica to overtake Sandy?

For Problems 11-32, use the geometric formulas given in this section to help solve the problems. (Objective 3 ) If the total surface area of a right circular cone is \(65 \pi\) square feet, and a radius of the base is 5 feet long, find the slant height of the cone.