### Review Exercises

##### Use a Problem Solving Strategy

**Approach Word Problems with a Positive Attitude**

In the following exercises, solve.

How has your attitude towards solving word problems changed as a result of working through this chapter? Explain.

Did the Problem Solving Strategy help you solve word problems in this chapter? Explain.

**Use a Problem Solving Strategy for Word Problems**

In the following exercises, solve using the problem-solving strategy for word problems. Remember to write a complete sentence to answer each question.

Three-fourths of the people at a concert are children. If there are $87$ children, what is the total number of people at the concert?

There are $9$ saxophone players in the band. The number of saxophone players is one less than twice the number of tuba players. Find the number of tuba players.

Reza was very sick and lost $\text{15\%}$ of his original weight. He lost $27$ pounds. What was his original weight?

Dolores bought a crib on sale for $\text{\$350}.$ The sale price was $\text{40\%}$ of the original price. What was the original price of the crib?

**Solve Number Problems**

In the following exercises, solve each number word problem.

Twice the difference of a number and ten is fifty-four. Find the number.

The sum of two consecutive integers is $-135.$ Find the numbers.

##### Solve Money Applications

**Solve Coin Word Problems**

In the following exercises, solve each coin word problem.

Francie has $\text{\$4.35}$ in dimes and quarters. The number of dimes is $5$ more than the number of quarters. How many of each coin does she have?

Scott has $\text{\$0.39}$ in pennies and nickels. The number of pennies is $8$ times the number of nickels. How many of each coin does he have?

Paulette has $\text{\$140}$ in $\text{\$5}$ and $\text{\$10}$ bills. The number of $\text{\$10}$ bills is one less than twice the number of $\text{\$5}$ bills. How many of each does she have?

Lenny has $\text{\$3.69}$ in pennies, dimes, and quarters. The number of pennies is $3$ more than the number of dimes. The number of quarters is twice the number of dimes. How many of each coin does he have?

**Solve Ticket and Stamp Word Problems**

In the following exercises, solve each ticket or stamp word problem.

A church luncheon made $\text{\$842}.$ Adult tickets cost $\text{\$10}$ each and children’s tickets cost $\text{\$6}$ each. The number of children was $12$ more than twice the number of adults. How many of each ticket were sold?

Tickets for a basketball game cost $\text{\$2}$ for students and $\text{\$5}$ for adults. The number of students was $3$ less than $10$ times the number of adults. The total amount of money from ticket sales was $\text{\$619}.$ How many of each ticket were sold?

Ana spent $\text{\$4.06}$ buying stamps. The number of $\text{\$0.41}$ stamps she bought was $5$ more than the number of $\text{\$0.26}$ stamps. How many of each did she buy?

Yumi spent $\text{\$34.15}$ buying stamps. The number of $\text{\$0.56}$ stamps she bought was $10$ less than $4$ times the number of $\text{\$0.41}$ stamps. How many of each did she buy?

##### Use Properties of Angles, Triangles, and the Pythagorean Theorem

**Use Properties of Angles**

In the following exercises, solve using properties of angles.

What is the complement of a $\text{61\xb0}$ angle?

Two angles are complementary. The smaller angle is $\text{24\xb0}$ less than the larger angle. Find the measures of both angles.

Two angles are supplementary. The larger angle is $\text{45\xb0}$ more than the smaller angle. Find the measures of both angles.

**Use Properties of Triangles**

In the following exercises, solve using properties of triangles.

The measures of two angles of a triangle are $22$ and $85$ degrees. Find the measure of the third angle.

One angle of a right triangle measures $41.5$ degrees. What is the measure of the other small angle?

One angle of a triangle is $\text{30\xb0}$ more than the smallest angle. The largest angle is the sum of the other angles. Find the measures of all three angles.

One angle of a triangle is twice the measure of the smallest angle. The third angle is $\text{60\xb0}$ more than the measure of the smallest angle. Find the measures of all three angles.

In the following exercises, $\text{\Delta}ABC$ is similar to $\text{\Delta}XYZ.$ Find the length of the indicated side.

side $b$

**Use the Pythagorean Theorem**

In the following exercises, use the Pythagorean Theorem to find the length of the missing side. Round to the nearest tenth, if necessary.

In the following exercises, solve. Approximate to the nearest tenth, if necessary.

Sergio needs to attach a wire to hold the antenna to the roof of his house, as shown in the figure. The antenna is $8$ feet tall and Sergio has $10$ feet of wire. How far from the base of the antenna can he attach the wire?

Seong is building shelving in his garage. The shelves are $36$ inches wide and $15$ inches tall. He wants to put a diagonal brace across the back to stabilize the shelves, as shown. How long should the brace be?

##### Use Properties of Rectangles, Triangles, and Trapezoids

**Understand Linear, Square, Cubic Measure**

In the following exercises, would you measure each item using linear, square, or cubic measure?

height of a tree

length of a highway

In the following exercises, find

- ⓐ the perimeter
- ⓑ the area of each figure

**Use Properties of Rectangles**

In the following exercises, find the ⓐ perimeter ⓑ area of each rectangle

The length of a rectangle is $36$ feet and the width is $19$ feet.

A sidewalk in front of Kathy’s house is in the shape of a rectangle $4$ feet wide by $45$ feet long.

A rectangular room is $16$ feet wide by $12$ feet long.

In the following exercises, solve.

Find the length of a rectangle with perimeter of $220$ centimeters and width of $85$ centimeters.

Find the width of a rectangle with perimeter $39$ and length $11.$

The width of a rectangle is $45$ centimeters. The area is $2700$ square centimeters. What is the length?

The length of a rectangle is $12$ centimeters more than the width. The perimeter is $74$ centimeters. Find the length and the width.

The width of a rectangle is $3$ more than twice the length. The perimeter is $96$ inches. Find the length and the width.

**Use Properties of Triangles**

In the following exercises, solve using the properties of triangles.

Find the area of a triangle with base $33$ centimeters and height $21$ centimeters.

If a triangular courtyard has sides $9$ feet and $12$ feet and the perimeter is $32$ feet, how long is the third side?

A tile in the shape of an isosceles triangle has a base of $6$ inches. If the perimeter is $20$ inches, find the length of each of the other sides.

Find the length of each side of an equilateral triangle with perimeter of $81$ yards.

The perimeter of a triangle is $59$ feet. One side of the triangle is $3$ feet longer than the shortest side. The third side is $5$ feet longer than the shortest side. Find the length of each side.

One side of a triangle is three times the smallest side. The third side is $9$ feet more than the shortest side. The perimeter is $39$ feet. Find the lengths of all three sides.

**Use Properties of Trapezoids**

In the following exercises, solve using the properties of trapezoids.

The height of a trapezoid is $5$ yards and the bases are $7$ and $10$ yards. What is the area?

A flag is shaped like a trapezoid with height $62$ centimeters and the bases are $91.5$ and $78.1$ centimeters. What is the area of the flag?

##### Solve Geometry Applications: Circles and Irregular Figures

**Use Properties of Circles**

In the following exercises, solve using the properties of circles. Round answers to the nearest hundredth.

A circular fountain has radius $8$ feet. Find the

- ⓐ circumference
- ⓑ area of the fountain

Find the radius of a circle with circumference $345.4$ centimeters

**Find the Area of Irregular Figures**

In the following exercises, find the area of each shaded region.

##### Solve Geometry Applications: Volume and Surface Area

**Find Volume and Surface Area of Rectangular Solids**

In the following exercises, find the

- ⓐ volume
- ⓑ surface area of the rectangular solid

a rectangular solid with length $14$ centimeters, width $4.5$ centimeters, and height $10$ centimeters

a cube with sides that are $3$ feet long

a rectangular carton with length $32$ inches, width $18$ inches, and height $10$ inches

**Find Volume and Surface Area of Spheres**

In the following exercises, find the

- ⓐ volume
- ⓑ surface area of the sphere.

a sphere with radius $12$ meters

a soccer ball with radius $22$ centimeters

**Find Volume and Surface Area of Cylinders**

In the following exercises, find the

- ⓐ volume
- ⓑ surface area of the cylinder

a cylinder with diameter $18$ inches and height $40$ inches

a cylindrical pylon with diameter $0.8$ feet and height $2.5$ feet

**Find Volume of Cones**

In the following exercises, find the volume of the cone.

a cone with height $24$ feet and radius $8$ feet

a cone-shaped pile of gravel with diameter $6$ yards and height $5$ yards

##### Solve a Formula for a Specific Variable

**Use the Distance, Rate, and Time Formula**

In the following exercises, solve using the formula for distance, rate, and time.

Gus rode his bike for $1\frac{1}{2}$ hours at $8$ miles per hour. How far did he ride?

Jack is driving from Bangor to Portland at a rate of $68$ miles per hour. The distance is $107$ miles. To the nearest tenth of an hour, how long will the trip take?

Jasmine took the bus from Pittsburgh to Philadelphia. The distance is $305$ miles and the trip took $5$ hours. What was the speed of the bus?

**Solve a Formula for a Specific Variable**

In the following exercises, use the formula $d=rt.$

Solve for $r\text{:}$

- ⓐ when $d=750$ and $t=15$
- ⓑ in general

In the following exercises, use the formula $A=\frac{1}{2}bh.$

Solve for $h\text{:}$

- ⓐ when $A=48$ and $b=8$
- ⓑ in general

In the following exercises, use the formula $I=Prt.$

Solve for the principal, $P,$ for:

- ⓐ$\phantom{\rule{0.2em}{0ex}}I=\text{\$720}$, $r=\text{4\%}$, $t=3\phantom{\rule{0.2em}{0ex}}\text{years}$
- ⓑ in general

Solve for the time, $t$ for:

- ⓐ$\phantom{\rule{0.2em}{0ex}}I=\text{\$3630}$, $P=\text{\$11,000}$, $r=5.5\%$
- ⓑ in general

In the following exercises, solve.

Solve the formula $2x+y=15$ for $y\text{:}$

- ⓐ when $x=\mathrm{-5}$
- ⓑ in general

Solve $180=a+b+c$ for $a.$

Solve the formula $-3x+y=\mathrm{-6}$ for $y.$

Solve the formula $V=LWH$ for $H.$

Describe how you have used two topics from this chapter in your life outside of math class during the past month.