Open-Ended Application Problems Chapter Questions
- List one strategy for solving a problem.
2. How would you define a consecutive integer?
3. What is the formula for perimeter, area of a rectangle, area of a triangle?
- What relationship will help when solving percent problems?
- List an example of a mixture type of problem.
- What must be true of an object in uniform motion?
- What is work rate?
- What type of angles measure up to 90 degrees?
Open-Ended Application Problem Chapter Problems
Number Problems
Classwork
1)List three consecutive integers.
2)List four consecutive odd integers.
3)One number is 5 greater than another. If the lesser number is added to two times the greater number, the sum is 40. Find the numbers.
4)One number is 7 less than another. If the greater number is subtracted from three times the lesser number, the difference is 163. Find the greater number.
5)Find the largest of three consecutive even integers whose sum is 24.
6)Find two consecutive integers whose sum is 61.
7)The lengths of the sides of a triangle are consecutive integers. The perimeter is 36 meters. Find the length of the largest side.
8)The lengths of the sides of a triangle are consecutive odd integers. The perimeter is 81 meters. Find the length of all the sides.
9)Johnny has 7 less than three times as many pizza deliveries as when he started his route. If he currently has 56 stops, how many did he start with?
10)There are 68 marbles in a jar that contains only blue and red marbles. The number of blue marbles is 4 less than 5 times the number of red marbles. How many red marbles are in the jar?
Homework
11)List five consecutive integers.
12)List four consecutive even integers.
13)One number is 35 less than another number. If the greater number is added to four times the lesser number, the sum is 100. Find the numbers.
14)One number is 8 more than another. If the greater number is added to five times the lesser number, their sum is 44. Find the greater number.
15)Find the smallest of three consecutive even integers whose sum is 99.
16)Find two consecutive even integers whose sum is 442.
17)The lengths of the sides of a triangle are consecutive integers. The perimeter is 15 meters. Find the length of the largest side.
18)The lengths of the sides of a triangle are consecutive even integers. The perimeter is 42 meters. Find the length of all the sides.
19)Mary has 3 more than three times as many shopping bags as when she started shopping at the mall hours ago. If she currently has 21 bags, how many did she start with?
20)There are 300 marbles in a jar that contains only blue and red marbles. The number of blue marbles is 20 less than 4 times the number of red marbles. How many red marbles are in the jar?
Age Problems
Classwork
Complete the table for each:
21)Joanna is 5 years older than her cat. Next year she will be three times as old as her cat will be. How old is her cat?
22)Eric is now ten years older than his niece Michelle. In five years, Eric will be four times Michelle’s present age. Find the age that Eric will be in five years.
23)In four years, Billy will be twice the age of Diana. If he is now seven years older than her, what is the age of each person now?
Write an Open Sentence for the following:
24)Tina is twice as old as Shelly. The sum of their ages is 65. How old is Tina?
25)Shelly is four times as young as Martha. The sum of their ages is 99. How old is Martha?
26)The daughter is 30 years younger than her mother. The sum of their ages is 72. How old is mom?
Solve:
27)Ricky’s age is nine years greater than twice Bobby’s age. If the sum of their ages is 21, how old are the boys?
28)Julie’s age is 15 years less than three times Frank’s age. If the sum of their ages is 5, how old is Frank?
29)There are three brothers in a store. Each brother is two years older than the next. The oldest brother is twice as old as the youngest brother. What is the age of the brothers?
30)There are five sisters at home. Each sister is three years older than the next. The oldest sister is four times the age of the youngest sister. What is the age of the oldest sister?
Homework
Complete the table for each:
31)Linda is 6 years older than her hamster. Next year she will be 4 times as old as the hamster. How old is Linda?
32)John is now twelve years older than his brother Timmy. In two years, John will be five times Timmy’s age. Find the age Timmy will be in two years.
33)In three years, Jenna will be two times the age of Hannah. If Jenna is now seven years older than Hannah, how old will they both be?
Write an Open Sentence for the following:
34) Bobby is three times as old as Kelly. The sum of their ages is 46. How old is Bobby?
35) Lisa is three times as young as Jackie. The sum of their ages is 110. How old is Jackie?
36)The son is three times younger than his father. The sum of their ages is 40. How old is the son?
Solve:
37)Tammy’s age is seven years greater than four times Jordan’s age. If the sum of their ages is 57, how old are the girls?
38)Lauren’s age is 11 years more than four times Robert’s age. If the difference of the smaller age from the larger age is 26, how old is Lauren?
39)There are four brothers in a store. Each brother is two years older than the next. The youngest brother is three times as young as the oldest brother. What is the age of the brothers?
40)There are five sisters at home. Each sister is one year older than the next. The oldest sister is five times the age of the youngest sister. What is the age of the third youngest sister?
Geometry Problems
Classwork
41)What is the perimeter of a square with one side length of 4?
42)What is the perimeter of a triangle with side lengths of 5,7, and 9?
43)What is the area of a rectangle with side lengths of 4 and 8?
44)What is the area of a triangle with a base of 4 and a height of 8?
45)A square has its side tripled in length. How much does the area of the square increase?
46)The length of a pool is two more feet than twice the width. The area of the pool is 36 feet. What is the length of the garden in terms of width?
47)A kitchen floor’s length is 4 feet less than five times its width. The area of the kitchen is 100 feet. What is the length of the kitchen in terms of the width?
48)The measure of the perimeter of a square is 16a + 40b. What is the measure of the area of the square?
Find the area of the white region below (not green):
49)
50)
Homework
51)What is the perimeter of a square with one side length of 7?
52)What is the perimeter of a triangle with side lengths of 8, 9 and 10?
53)What is the area of a rectangle with side lengths of 10 and 12?
54)What is the area of a triangle with a base of 10 and a height of 12?
55)A square has its side quadrupled in length. How much does the area of the square increase?
56)The length of a pool is four more feet than three times the width. The area of the pool is 56 feet. What is the length of the garden in terms of width?
57)A kitchen floor’s length is 8 feet less than five times its width. The area of the kitchen is 69 feet. What is the length of the kitchen in terms of width?
58)The measure of the perimeter of a square is 4a + 28b. What is the measure of the area of the square?
Find the area of the white region below (not green):
59)
60)
Percent Problems
Classwork
61)A shirt is on the rack for $27.00. There is a 15% discount that day in the store. What amount of money will come off of the original price?
62)A dress is on sale for $60.00 after a 50% discount is taken off. What is the regular price of the dress?
63)A new bike is $175.00 in the store. There is a 7% tax in the store. How much will you pay for the bike?
64)The bill at the restaurant is $46. You want to leave a 30% tip. How much will you leave for the tip?
65)The first store has a TV for $1100 on sale 30% off. A second store has the same TV for $1100 on sale for 10% with an additional 20% with your coupon you have. Which store has the better deal?
66)A DVD movie price increases from $15.00 to $24.00. What is the percent of increase?
67)How much is the percent of change when the original price of a bathing suit is $300 and the new price is $50?
68)How much will simple interest be if the Johnson’s invest $30,000 at 5% interest rate for 6 years?
69)The Smiths paid $15,000 in closing costs when buying their first new home. If this amount represents 7% of the purchase price, how much did they pay for their home?
70)Karin invested part of $9,000 in one bank account that pays 5% simple annual interest and the rest in an account that pays 9% simple annual interest. How much money is invested in each account if the total annual income is $600?
Homework
71)A skirt is on the rack for $48.00. There is a 43% discount that day in the store. What amount of money will come off of the original price?
72)A suit is on sale for $67.72 after a 50% discount is taken off. What is the regular price of the suit?
73)A new grill is $175.50 in the store. There is a 7.75% tax in the store. How much will you pay for the grill?
74)The bill at the restaurant is $25.00. You want to leave a 15% tip. How much will you leave for the tip?
75)The first store has a computer for $2100 on sale 30% off. A second store has the same computer for $2100 on sale for 10% with an additional 40% with your coupon you have. Which store has the better deal?
76)An iTunes movie price increases from $10.00 to $14.00. What is the percent of increase?
77)How much is the percent of change when the original price of a dress is $200 and the new price is $50?
78)How much will simple interest be if the Linders invest $30,000 at 9% interest rate for 4 years?
79)The Farleys paid $10,000 in closing costs when buying their first new home. If this amount represents 5% of the purchase price, how much did they pay for their home?
80)Thomas invested part of $10,000 in one bank account that pays 5% simple annual interest and part in an account that pays 9% simple annual interest. How much money is invested in each account if the total annual income is $625?
Mixture Problems
Classwork
Set Up the following problems in the table:
81)Andrew bought some apples worth $0.98 and some bananas worth $0.57. He bought 24 fruit items in total and paid $15.00 for them. How many apples and bananas did he buy?
82)Phil was conducting an experiment with a 30L solution that was 12% salt. How much water must be added to make it a 5% salt solution?
Solve:
83)Alexis was conducting an experiment with a 24L solution that was 15% salt. How much water must be added to make it a 7% salt solution?
84)A ticket booth sold 226 tickets and collected $843 in ticket sales. Adult tickets are $5.50 and child tickets are $1.50. How many tickets for adults were sold?
85) A 12L solution is 50% oil. How much water must be added to produce a solution that is 45% oil?
86) Madison has three times as many dimes as pennies in her piggy bank. If the dimes and pennies total $8.37, how many pennies does she have?
87)The register at the grocery store has 15 bills in $5 and $10 denominations. The value of the money in the register is $100. How many $10 bills are in the register?
88)How many gallons of a 3% salt solution must be mixed with 50 gallons of a 7% solution to obtain a 5% solution?
89)A 50 ml after-shave lotion at 30% alcohol is mixed with 30 ml of pure water. What is the percentage of alcohol in the new solution?
90)How many pounds of chocolate worth $1.20 a pound must be mixed with 10 pounds of chocolate worth 90 cents a pound to produce a mixture worth $1.00 a pound?
Homework
Set Up the following problems in the table:
91)Susan bought some peanuts worth $0.64 and some cashews worth $0.32. He bought 26 nuts in total and paid $14.40 for them. How many peanuts did he buy?
92)Tiffany was conducting an experiment with a 44L solution that was 13% salt. How much water must be added to make it a 2% salt solution?
Solve:
93)Alexa was conducting an experiment with a 48L solution that was 22% salt. How much water must be added to make it a 15% salt solution?
94)How many pounds of chocolate worth $4.50 a pound must be mixed with 10 pounds of chocolate worth $3.90 a pound to produce a mixture worth $4.00 a pound?
95)How many gallons of a 4% salt solution must be mixed with 20 gallons of a 10% solution to obtain a 7% solution?
96)Margaret has 3 more than 2 times as many dimes as pennies in her piggy bank. If the dimes and pennies total $0.75, how many pennies does she have?
97)Five hundred tickets were sold for a certain music concert. The tickets for the adults and children sold for $7.50 and $4.00, respectively, and the total receipts for the performance were $3,312.50. How many child tickets were sold?
98)How many liters of 20% alcohol solution should be added to 40 liters of a 50% alcohol solution to make a 30% solution?
99)Sterling Silver is 92.5% pure silver. How many grams of Sterling Silver must be mixed to a 90% Silver alloy to obtain a 500g of a 91% Silver alloy?
100)How many Kilograms of Pure water is to be added to 100 Kilograms of a 30% saline solution to make it a 10% saline solution.
Uniform Motion Problems
Classwork
101)Two airplanes leave from the same airport at the same time traveling to Hawaii. The faster plane arrives in 5 hours. The slower plane arrives in 15 hours. The slower plane travels at an average speed that is 25km/h slower than the faster plane. What is the average speed of the faster plane?
102)Ariel and Sam are 545 meters apart. Ariel walks towards Sam at a rate of 1.7 m/s and Sam starts running towards Ariel. What is Sam’s rate of travel is she reaches Ariel in 2 minutes?
103)Fred is a member of the swim team at school. On Tuesday he swam towards the far side of the pool at a rate of 4.6 m/min and on the return back he swam at a rate of 3.4 m/min. If he took 7 minutes to swim the entire distance, how long is the pool?
104)Sarah made the trip in 10 hours, but it only took Alice 8 hours to make the same trip. Find Sarah’s rate of speed if Alice's rate was 3 mph more than Sarah's rate.
105)The bus made the trip in 6 hours, but the train took only 4 hours for the same trip. Find the rate of the bus if the train's rate of speed is 25 mph more than the bus' rate.
106)A car and a bus set out at 2 p.m. from the same point, headed in the same direction. The average speed of the car is 30 mph slower than twice the speed of the bus. In two hours, the car is 20 miles ahead of the bus. Find the rate of the car.
107)Two trains start from the same station and run in opposite directions. One runs at an average rate of 40 miles per hour, and the other at 65 miles per hour. In how many hours will they be 315 miles apart?
108)Mr. Williams starts out in his auto traveling 30 miles per hour. Four hours later Mr. Speedster starts out from the same point at 60 miles per hour to overtake Mr. Williams. In how many hours will he be overtaken?
109)A pilot flew to Newark and back. The average speed going was 320 mph. The average speed returning was 480 mph. Find the distance to Newark if the total flying time was 5h.
110)A car and a bus set out at 3 p.m. from the same point headed in the same direction. The average speed of the car is twice the average speed of the bus. In 2 h, the car is 68 mi ahead of the bus. Find the rate of the car.
Homework
111)Two sail boats leave from the same port at the same time traveling to Jamaica. The faster boat arrives in 4 hours. The slower boat arrives in 6 hours. The slower boat travels at an average speed that is 2km/h slower than the faster boat. What is the average speed of the faster boat?
112)Miriam and Doug are 700 meters apart. Doug walks towards Miriam at a rate of 3.4 m/s and Miriam starts running towards Doug. What is Miriam's rate of travel if she reaches Doug in 1.4 minutes?
113)Francine is a member of the track team at school. On Thursday he ran towards the far side of the track at a rate of 3.5 m/hr and on the return back he ran at a rate of 5 m/hr. If he took 10 minutes to run the entire distance, how long is the track?
114)Shannon made the trip in 20 hours, but it only took Alicia 16 hours to make the same trip. Find Alicia’s rate if her rate was 6 mph more than Shannon's rate.
115)The bus made the trip in 8hours, but the train took only 3 hours for the same trip. Find the rate of the bus if the train's rate of speed is 35 mph more than the bus' rate.
116)A car and a bus set out at 5 p.m. from the same point, headed in the same direction. The average speed of the car is 40 mph slower than twice the speed of the bus. In three hours, the bus is 10 miles ahead of the car. Find the rate of the car.
117)Two trains start from the same station and run in opposite directions. One runs at an average rate of 50 miles per hour, and the other at 70 miles per hour. In how many hours will they be 200 miles apart?
118)Mr. Sanford starts out in his truck traveling 40 miles per hour. Three hours later Mr. Shocker starts out from the same point at 65 miles per hour to overtake Mr. Williams. In how many hours will he be overtaken?