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Word problems and geometry exercises · Physics Playground

Word problems and geometry

102 problems with worked solutions, from Prealgebra and Elementary Algebra.

Start with a random one

Learn it first: Direct, Inverse & Square Proportion

Prealgebra9.1 Use a Problem Solving Strategy

Example 9.1Pete bought a shirt on sale for $18, which is one-half the original price. What was the original price of the shirt?Plus a twin to try
Example 9.2Yash brought apples and bananas to a picnic. The number of apples was three more than twice the number of bananas. Yash brought 11 apples to the picnic. How many bananas did he bring?Plus a twin to try
Example 9.3Nga's car insurance premium increased by $60, which was 8% of the original cost. What was the original cost of the premium?Plus a twin to try
Example 9.4The difference of a number and six is 13. Find the number.Plus a twin to try
Example 9.5The sum of twice a number and seven is 15. Find the number.Plus a twin to try
Example 9.6One number is five more than another. The sum of the numbers is twenty-one. Find the numbers.Plus a twin to try
Example 9.7The sum of two numbers is negative fourteen. One number is four less than the other. Find the numbers.Plus a twin to try
Example 9.8One number is ten more than twice another. Their sum is one. Find the numbers.Plus a twin to try
Example 9.9The sum of two consecutive integers is 47. Find the numbers.Plus a twin to try
Example 9.10Find three consecutive integers whose sum is 42.Plus a twin to try

Prealgebra9.2 Solve Money Applications

Example 9.11Adalberto has $2.25 in dimes and nickels in his pocket. He has nine more nickels than dimes. How many of each type of coin does he have?Plus a twin to try
Example 9.12Maria has $2.43 in quarters and pennies in her wallet. She has twice as many pennies as quarters. How many coins of each type does she have?Plus a twin to try
Example 9.13Danny has $2.14 worth of pennies and nickels in his piggy bank. The number of nickels is two more than ten times the number of pennies. How many nickels and how many pennies does Danny have?Plus a twin to try
Example 9.14At a school concert, the total value of tickets sold was $1,506. Student tickets sold for $6 each and adult tickets sold for $9 each. The number of adult tickets sold was 5 less than three times the number of student…Plus a twin to try
Example 9.15Monica paid $10.44 for stamps she needed to mail the invitations to her sister's baby shower. The number of 49-cent stamps was four more than twice the number of 8-cent stamps. How many 49-cent stamps and how many…Plus a twin to try

Prealgebra9.3 Use Properties of Angles, Triangles, and the Pythagorean Theorem

Example 9.16An angle measures 40°. Find ⓐ its supplement, and ⓑ its complement.Plus a twin to try
Example 9.17Two angles are supplementary. The larger angle is 30° more than the smaller angle. Find the measure of both angles.Plus a twin to try
Example 9.18The measures of two angles of a triangle are 55° and 82°. Find the measure of the third angle.Plus a twin to try
Example 9.19One angle of a right triangle measures 28°. What is the measure of the third angle?Plus a twin to try
Example 9.20The measure of one angle of a right triangle is 20° more than the measure of the smallest angle. Find the measures of all three angles.Plus a twin to try
Example 9.21ΔABC and ΔXYZ are similar triangles. The lengths of two sides of each triangle are shown. Find the lengths of the third side of each triangle.With a figurePlus a twin to try
Example 9.22Use the Pythagorean Theorem to find the length of the hypotenuse.With a figurePlus a twin to try
Example 9.23Use the Pythagorean Theorem to find the length of the longer leg.With a figurePlus a twin to try
Example 9.24Kelvin is building a gazebo and wants to brace each corner by placing a 10-inch wooden bracket diagonally as shown. How far below the corner should he fasten the bracket if he wants the distances from the corner to…With a figurePlus a twin to try

Prealgebra9.4 Use Properties of Rectangles, Triangles, and Trapezoids

Example 9.25For each item, state whether you would use linear, square, or cubic measure: ⓐ amount of carpeting needed in a room ⓑ extension cord length ⓒ amount of sand in a sandbox ⓓ length of a curtain rod ⓔ amount of flour in…Plus a twin to try
Example 9.26Each of two square tiles is 1 square inch. Two tiles are shown together. ⓐ What is the perimeter of the figure? ⓑ What is the area?With a figurePlus a twin to try
Example 9.27The length of a rectangle is 32 meters and the width is 20 meters. Find ⓐ the perimeter, and ⓑ the area.Plus a twin to try
Example 9.28Find the length of a rectangle with perimeter 50 inches and width 10 inches.Plus a twin to try
Example 9.29The width of a rectangle is two inches less than the length. The perimeter is 52 inches. Find the length and width.Plus a twin to try
Example 9.30The length of a rectangle is four centimeters more than twice the width. The perimeter is 32 centimeters. Find the length and width.Plus a twin to try
Example 9.31The area of a rectangular room is 168 square feet. The length is 14 feet. What is the width?Plus a twin to try
Example 9.32The perimeter of a rectangular swimming pool is 150 feet. The length is 15 feet more than the width. Find the length and width.Plus a twin to try
Example 9.33Find the area of a triangle whose base is 11 inches and whose height is 8 inches.Plus a twin to try
Example 9.34The perimeter of a triangular garden is 24 feet. The lengths of two sides are 4 feet and 9 feet. How long is the third side?Plus a twin to try
Example 9.35The area of a triangular church window is 90 square meters. The base of the window is 15 meters. What is the window’s height?Plus a twin to try
Example 9.36The perimeter of an equilateral triangle is 93 inches. Find the length of each side.Plus a twin to try
Example 9.37Arianna has 156 inches of beading to use as trim around a scarf. The scarf will be an isosceles triangle with a base of 60 inches. How long can she make the two equal sides?Plus a twin to try
Example 9.38Find the area of a trapezoid whose height is 6 inches and whose bases are 14 and 11 inches.Plus a twin to try
Example 9.39Find the area of a trapezoid whose height is 5 feet and whose bases are 10.3 and 13.7 feet.Plus a twin to try
Example 9.40Vinny has a garden that is shaped like a trapezoid. The trapezoid has a height of 3.4 yards and the bases are 8.2 and 5.6 yards. How many square yards will be available to plant?Plus a twin to try

Prealgebra9.5 Solve Geometry Applications: Circles and Irregular Figures

Example 9.41A circular sandbox has a radius of 2.5 feet. Find the ⓐ circumference and ⓑ area of the sandbox.Plus a twin to try
Example 9.42A circular table has a diameter of four feet. What is the circumference of the table?Plus a twin to try
Example 9.43Find the diameter of a circle with a circumference of 47.1 centimeters.Plus a twin to try
Example 9.44Find the area of the shaded region.With a figurePlus a twin to try
Example 9.46A high school track is shaped like a rectangle with a semi-circle (half a circle) on each end. The rectangle has length 105 meters and width 68 meters. Find the area enclosed by the track. Round your answer to the…With a figurePlus a twin to try

Prealgebra9.6 Solve Geometry Applications: Volume and Surface Area

Example 9.47For a rectangular solid with length 14 cm, height 17 cm, and width 9 cm, find the ⓐ volume and ⓑ surface area.Plus a twin to try
Example 9.48A rectangular crate has a length of 30 inches, width of 25 inches, and height of 20 inches. Find its ⓐ volume and ⓑ surface area.Plus a twin to try
Example 9.49A cube is 2.5 inches on each side. Find its ⓐ volume and ⓑ surface area.Plus a twin to try
Example 9.50A notepad cube measures 2 inches on each side. Find its ⓐ volume and ⓑ surface area.Plus a twin to try
Example 9.51A sphere has a radius 6 inches. Find its ⓐ volume and ⓑ surface area.Plus a twin to try
Example 9.52A globe of Earth is in the shape of a sphere with radius 14 centimeters. Find its ⓐ volume and ⓑ surface area. Round the answer to the nearest hundredth.Plus a twin to try
Example 9.53A cylinder has height 5 centimeters and radius 3 centimeters. Find the ⓐ volume and ⓑ surface area.Plus a twin to try
Example 9.54Find the ⓐ volume and ⓑ surface area of a can of soda. The radius of the base is 4 centimeters and the height is 13 centimeters. Assume the can is shaped exactly like a cylinder.Plus a twin to try
Example 9.55Find the volume of a cone with height 6 inches and radius of its base 2 inches.Plus a twin to try
Example 9.56Marty’s favorite gastro pub serves french fries in a paper wrap shaped like a cone. What is the volume of a conic wrap that is 8 inches tall and 5 inches in diameter? Round the answer to the nearest hundredth.Plus a twin to try

Prealgebra9.7 Solve a Formula for a Specific Variable

Example 9.57Jamal rides his bike at a uniform rate of 12 miles per hour for 31/2 hours. How much distance has he traveled?Plus a twin to try
Example 9.58Rey is planning to drive from his house in San Diego to visit his grandmother in Sacramento, a distance of 520 miles. If he can drive at a steady rate of 65 miles per hour, how many hours will the trip take?Plus a twin to try
Example 9.59Solve the formula d=rt for t: ⓐ when d=520 and r=65ⓑ in general.Plus a twin to try
Example 9.60The formula for area of a triangle is A=1/2bh. Solve this formula for h: ⓐ when A=90 and b=15ⓑ in generalPlus a twin to try
Example 9.61Solve the formula I=Prt to find the principal, P: ⓐ when I=$5,600,r=4%,t=7yearsⓑ in generalPlus a twin to try
Example 9.62Solve the formula 3x+2y=18 for y: ⓐ when x=4ⓑ in generalPlus a twin to try
Example 9.63Solve the formula P=a+b+c for a.Plus a twin to try
Example 9.64Solve the equation 3x+y=10 for y.Plus a twin to try
Example 9.65Solve the equation 6x+5y=13 for y.Plus a twin to try

Elementary Algebra3.1 Use a Problem-Solving Strategy

Example 3.1Pilar bought a purse on sale for $18, which is one-half of the original price. What was the original price of the purse?Plus a twin to try
Example 3.2Ginny and her classmates formed a study group. The number of girls in the study group was three more than twice the number of boys. There were 11 girls in the study group. How many boys were in the study group?Plus a twin to try
Example 3.5One number is five more than another. The sum of the numbers is 21. Find the numbers.Plus a twin to try
Example 3.10Find three consecutive even integers whose sum is 84.Plus a twin to try
Example 3.11A married couple together earns $110,000 a year. The wife earns $16,000 less than twice what her husband earns. What does the husband earn?Plus a twin to try

Elementary Algebra3.2 Solve Percent Applications

Example 3.12Translate and solve: What number is 35% of 90?Plus a twin to try
Example 3.13Translate and solve: 6.5% of what number is $1.17?Plus a twin to try
Example 3.14Translate and solve: 144 is what percent of 96?Plus a twin to try
Example 3.15Dezohn and his girlfriend enjoyed a nice dinner at a restaurant and his bill was $68.50. He wants to leave an 18% tip. If the tip will be 18% of the total bill, how much tip should he leave?Plus a twin to try
Example 3.18In 2011, the California governor proposed raising community college fees from $26 a unit to $36 a unit. Find the percent increase. (Round to the nearest tenth of a percent.)Plus a twin to try
Example 3.20Nathaly deposited $12,500 in her bank account where it will earn 4% interest. How much interest will Nathaly earn in 5 years? I=?P=$12,500r=4%t=5yearsPlus a twin to try
Example 3.21Loren loaned his brother $3,000 to help him buy a car. In 4 years his brother paid him back the $3,000 plus $660 in interest. What was the rate of interest? I=$660P=$3,000r=?t=4yearsPlus a twin to try
Example 3.22Eduardo noticed that his new car loan papers stated that with a 7.5% interest rate, he would pay $6,596.25 in interest over 5 years. How much did he borrow to pay for his car?Plus a twin to try
Example 3.25Adam’s art gallery bought a photograph at original cost $250. Adam marked the price up 40%. Find the ⓐ amount of mark-up and ⓑ the list price of the photograph.Plus a twin to try

Elementary Algebra3.3 Solve Mixture Applications

Example 3.29At a school concert, the total value of tickets sold was $1,506. Student tickets sold for $6 each and adult tickets sold for $9 each. The number of adult tickets sold was five less than three times the number of…Plus a twin to try
Example 3.30Galen sold 810 tickets for his church’s carnival for a total of $2,820. Children’s tickets cost $3 each and adult tickets cost $5 each. How many children’s tickets and how many adult tickets did he sell?Plus a twin to try
Example 3.31Monica paid $8.36 for stamps. The number of 41-cent stamps was four more than twice the number of two-cent stamps. How many 41-cent stamps and how many two-cent stamps did Monica buy?Plus a twin to try
Example 3.32Henning is mixing raisins and nuts to make 10 pounds of trail mix. Raisins cost $2 a pound and nuts cost $6 a pound. If Henning wants his cost for the trail mix to be $5.20 a pound, how many pounds of raisins and how…Plus a twin to try
Example 3.33Stacey has $20,000 to invest in two different bank accounts. One account pays interest at 3% per year and the other account pays interest at 5% per year. How much should she invest in each account if she wants to…Plus a twin to try

Elementary Algebra3.4 Solve Geometry Applications: Triangles, Rectangles, and the Pythagorean Theorem

Example 3.34The measures of two angles of a triangle are 55 and 82 degrees. Find the measure of the third angle.Plus a twin to try
Example 3.35The perimeter of a triangular garden is 24 feet. The lengths of two sides are four feet and nine feet. How long is the third side?Plus a twin to try
Example 3.38The measure of one angle of a right triangle is 20 degrees more than the measure of the smallest angle. Find the measures of all three angles.Plus a twin to try
Example 3.39Use the Pythagorean Theorem to find the length of the hypotenuse shown below.With a figurePlus a twin to try
Example 3.40Use the Pythagorean Theorem to find the length of the leg shown below.With a figurePlus a twin to try
Example 3.41Kelvin is building a gazebo and wants to brace each corner by placing a 10″ piece of wood diagonally as shown above. If he fastens the wood so that the ends of the brace are the same distance from the corner, what is…With a figurePlus a twin to try
Example 3.42The length of a rectangle is 32 meters and the width is 20 meters. What is the perimeter?Plus a twin to try
Example 3.45The width of a rectangle is two feet less than the length. The perimeter is 52 feet. Find the length and width.Plus a twin to try

Elementary Algebra3.5 Solve Uniform Motion Applications

Example 3.48An express train and a local train leave Pittsburgh to travel to Washington, D.C. The express train can make the trip in 4 hours and the local train takes 5 hours for the trip. The speed of the express train is 12…Plus a twin to try
Example 3.49Christopher and his parents live 115 miles apart. They met at a restaurant between their homes to celebrate his mother’s birthday. Christopher drove 1.5 hours while his parents drove 1 hour to get to the restaurant.…Plus a twin to try
Example 3.50Two truck drivers leave a rest area on the interstate at the same time. One truck travels east and the other one travels west. The truck traveling west travels at 70 mph and the truck traveling east has an average…Plus a twin to try
Example 3.51When Katie Mae walks to school, it takes her 30 minutes. If she rides her bike, it takes her 15 minutes. Her speed is three miles per hour faster when she rides her bike than when she walks. What are her walking…Plus a twin to try
Example 3.52Hamilton loves to travel to Las Vegas, 255 miles from his home in Orange County. On his last trip, he left his house at 2:00 pm. The first part of his trip was on congested city freeways. At 4:00 pm, the traffic…Plus a twin to try

Elementary Algebra3.6 Solve Applications with Linear Inequalities

Example 3.53Emma got a new job and will have to move. Her monthly income will be $5,265. To qualify to rent an apartment, Emma’s monthly income must be at least three times as much as the rent. What is the highest rent Emma will…Plus a twin to try
Example 3.54Dawn won a mini-grant of $4,000 to buy tablet computers for her classroom. The tablets she would like to buy cost $254.12 each, including tax and delivery. What is the maximum number of tablets Dawn can buy?Plus a twin to try
Example 3.55Pete works at a computer store. His weekly pay will be either a fixed amount, $925, or $500 plus 12% of his total sales. How much should his total sales be for his variable pay option to exceed the fixed amount of $925?Plus a twin to try
Example 3.56Sergio and Lizeth have a very tight vacation budget. They plan to rent a car from a company that charges $75 a week plus $0.25 a mile. How many miles can they travel and still keep within their $200 budget?Plus a twin to try
Example 3.57Elliot has a landscape maintenance business. His monthly expenses are $1,100. If he charges $60 per job, how many jobs must he do to earn a profit of at least $4,000 a month?Plus a twin to try
Example 3.58Brenda’s best friend is having a destination wedding and the event will last 3 days. Brenda has $500 in savings and can earn $15 an hour babysitting. She expects to pay $350 airfare, $375 for food and entertainment…Plus a twin to try