As we near the one hundredth day of school, here are 100 problems to challenge students in grades 3 and up.

Don’t forget to have students write their answer in a full sentence, check that they answered the correct question, and check that their answer is reasonable.

Visual models are a particularly useful strategy for these problems.


1) Marcus and Haley have 129 stamps altogether. If Marcus has 86 stamps, how many more stamps does he have than Haley?

 2) One Sunday, 681 people visited the zoo. Of these, 291 were men, 135 were women, and the rest were children. How many more adults than children visited the zoo that day?

 3) Mr. Chen picked 314 oranges from his tree. Of these, 19 were bad and thrown away. If he sold 218 oranges, how many did he have left?

 4) The difference between two numbers is 23. If the smaller number is 32, what is the bigger number?

 5) Kayla has 54 erasers. Scott has 21 less erasers than Kayla. How many erasers does Scott have?

 6) Peter has 21 fewer marbles than Nancy. If Peter has 43 marbles, how many marbles does Nancy have?

 7) The difference between two numbers is 38. If the bigger number is 76, what is the smaller number?

 8) Sue has 87 stickers. Perry has 48 stickers fewer than Sue but 16 stickers more than Kevin. How many stickers does Kevin have?

 9) There were 50 boys at the school play. If there were 23 more boys than girls, how many girls were there?

 10) Mason lives 7 miles away from the amusement park. Holly lives 5 times farther away than Mason. How far does Holly live from the amusement park?

 11) Nancy has 36 tunes on her iPod. That’s 3 times as many tunes as Juan has. How many tunes does Juan have?

 12) Jada has nine times as many baseball cards as Steve. If Jada has 54 baseball cards, how many baseball cards does Steve have?

 13) Weak Willy can only do 19 knee bends. Active Amy can do 4 times as many knee bends as Weak Willy. How many knee bends can Active Amy do?

 14) Skylar has 4 times as many books as Karen. If Skylar has 60 books, how many books does Karen have?

 15) A shopkeeper had 213 folders. He sold 178 folders and bundled the remaining folders into packs of 5. How many packs of folders did he get?

 16) Oliver has 9 pens. Bernard has three times as many pens as Oliver. How many more pens does Bernard have than Oliver?

 17) After giving 4 stickers to each of her 9 friends, Rose had 87 stickers left. How many stickers did she have at first?

 18) Les collected 302 bottle caps. He kept 232 bottle caps for himself and divided the rest among his 10 friends equally. How many bottle caps did each of his friends receive?

 19) Kenny had 41 erasers. He gave an equal number of erasers to each of his 3 cousins and had 29 erasers left. How many erasers did he give to each cousin?

 20) Angelica has $40 to buy her mother a birthday present. She buys flowers for $16 and a new pen set for $8. How much money does she have left?

 21) There were 11 boys at the library. If there were 5 times as many girls than boys, how many children were at the library?

 22) Mike and Paul have 48 coins together. If Mike has seven times as many coins as Paul, how many more coins does he have than Paul?

 23) Mrs. Drew buys 12 apples. She buys 3 times as many oranges as apples. She also buys 4 times as many cherries as oranges. How many more cherries than apples did she buy?

 24) Susan has 6 times as much money as Ted. If Susan has $250 more than Ted, how much money do they have in all?

 25) Mr. Rulaski gives $30 to Bailey and Jenny. If Bailey gets twice as much money as Jenny, how much will Jenny get?

 26) Dave has 7 times as many apples as oranges. If he has 56 apples and oranges together, how many more apples than oranges does he have?

 27) Sergio has 32 fewer pencils than Benny. If Sergio has 49 pencils, how many pencils do Sergio and Benny have together?

 28) Claire saved 53 dollars. That was 29 dollars less than Henry saved. Jill saved 68 dollars. How many more dollars did Henry save than Jill?

 29) Margo has three times as many marbles as jump ropes. If she has 44 marbles and jump ropes all together, how many marbles does she have?

 30) A grocer has 42 apples. 2/7 of them are red and the rest are green. How many of them are green?

 31) A nurse has some bandages. 4/9 of them are white and the rest are brown. If the nurse has 32 white bandages, how many brown bandages does she have?

 32) Scott has a bag of candies. 2/5 of the candies are red. 3/10 of the candies are green. If there are 12 red candies, how many green candies are in the bag?

 33) 5/7 of a group of students are boys. There are 18 more boys than girls. How many students are there all together?

 34) Mr. Samuel has 70 pennies in two jars. There are 40 more pennies in one jar than in the other. How many pennies are in each jar?

 35) Mrs. Washington made 36 cookies. She sold ¾ of them and gave 1/3 of the remainder to her neighbor. How many cookies did she have left for herself?

 36) After Jason spent 7/10 of his money and Marcus spent 5/6 of his money, they each had $15 left. How much money did they spend all together?

 37) Lisa and Ann had 130 hair clips all together. After Lisa gave away 3/8 of her hair clips, she had the same number of hair clips as Ann. How many more hair clips did Lisa have than Ann at first?

 38) Jill has some marbles. 2/7 of them are red and the rest are blue. If Jill has 32 red marbles, how many blue marbles does she have?

 39) I have 16 tomatoes in my garden. If 2/5 of all the vegetables in my garden are tomatoes, how many vegetables do I have in my garden?

 40) Weak Willy did 44 sit-ups in two days. He did 12 more sit-ups on one day than on the other. How many sit-ups did he do each day?

 41) Active Amy made 45 healthy snacks. She shared 3/5 of them with friends and gave 1/3 of the remainder to Weak Willy. How many snacks did she have left for herself?

 42) Two numbers have a sum of 47. Their difference is 5. What are the two numbers?

 43) Ed and Sabrina spent $72 in Publix this week. If Ed spent $6 less than Sabrina, how much did Sabrina spend?

 44) Juan, Carlos, and Roy shared a pack of gum. There were 43 pieces of gum in the pack. Carlos had 5 more pieces than Juan and 3 more pieces than Roy. How many pieces of gum did Roy have?

 45) Mrs. Cook has 3 bags of oranges. Each bag contains 12 oranges. If she takes all the oranges out of the bags and puts an equal amount on each of 6 plates, how many oranges will there be on each plate?

 46) Peter has 19 white balloons, 23 red balloons, and 18 yellow balloons. He has half as many balloons as Paul. How many balloons does Paul have?

 47) Don has 26 bottle caps. Jack has three times as many bottle caps as Don but half as many bottle caps as Tom. How many bottle caps does Tom have?

 48) A sum of $60 is shared among 2 boys and a girl. If the girl gets twice the amount that each boy gets, how much money does each boy get?

 49) Jim and Dan have $24 altogether. If Jim gives $2 to Dan, he will have three times as much money as Dan. How much money does Jim have?

 50) There are three fish tanks, A, B, and C. B weighs six times as much as A and twice as much as C. If C is 36 pounds heavier than A, find the total weight of A,B, and C.

 51) A rectangle has a length of 17 cm and a perimeter of 50 cm. What is its area?

 52) Jill had 72 candies. After giving the same number of candies to each of her three brothers, she had 48 candies left. How many candies did she give to each brother?

 53) James has 122 new songs on his iPhone. After listening to the same number of songs each day for a week, he had 66 songs that he had not heard. How many songs did he listen to each day?

 54) Mr. Wayne was three times as old as Colleen 5 years ago. Their total age is now 42 years. How old is Colleen now?

 55) Cathy spent 4/5 of her money while Josie spent ½ of her money. Both of them had the same amount of money left. If Josie had $35 left, how much did Cathy have at first?

 56) Peter spent 1/3 of his money on a toy car and 2/3 of the remainder on a toy boat. He had $6 left. How much money did he spend altogether?

 57) A tank is 3/5 full with water. If 30 liters more water are needed to fill the tank completely, find the capacity of the tank.

 58) Sam bought 3 shirts and 2 pairs of pants for $67.30. Each pair of pants costs $2.40 more than each shirt. What is the cost of one pair of pants?

 59) Sam had $85 and John had $220. They were each given an equal amount of money. Then John had twice as much money as Sam. How much money did each boy receive?

 60) Kate cut a 100 foot rope into two pieces. One piece was 5 feet longer than 4 times the length of the other. Find the length of each piece.

 61) One half of a number increased by 16 is four less than two thirds of the number. Find the number.

 62) Mr. Davis made some cookies. He sold ¼ of them and gave ¼ of the remainder to his neighbor. If he gave his neighbor 18 cookies, how many cookies did he make?

 63) Karen promised Sara that she would give half of her remaining money to Sara after giving 7/8 of it to her favorite charity. If Karen gave $672 to her favorite charity, how much money will Sara receive?

 64) Benjamin found a bag of money. He decided to give ½ of the money to his best friend, ¼ of the money to his sister, 1/8 of the money to his mother, and 1/16 of the money to his dad. The amount of money that was left was $1.25. How much money was in the bag when Benjamin found it?

 65) Gary works at Ghosts and Goblins, a Halloween store. He puts orange, black, and white candies in boxes. After he fills a box, ¼ is orange, 1/6 is black, and 21 are white. How many candies does Gary put in each box?

 66) Alex, Ben, and David ran in a race, but none of them reached the finish line. Ben ran 5 times as far as Alex before he stopped. David stopped 1 km before the finish line and he ran 3 km less than twice the distance Ben ran. If the three of them ran 21 km, how long was the race?

 67) The school secretary bought a large batch of pencils. She gave 9 to the principal and then gave 20% of what was left to the first grade teachers. She kept ½ of the remaining pencils and divided the other ½ among four grade level teams, each of whom received 21 pencils. How many pencils were in the original batch?

 68) Ray gave 10% of his balloons to Silvia, 15% of them to Mina, 10% of them to Wendy, and had 13 balloons left. How many balloons did he give away all together?

 69) Jimmy read 2/15 of a book on Monday, 1/3 of it on Tuesday, 2/9 of it on Wednesday, and ¾ of the remainder on Thursday. If he still had 14 pages left to read on Friday, how many pages were there in the book?

 70) Andrew had 200 postcards. 40% of them were U.S. postcards, and the rest were overseas postcards. He bought another 100 postcards and the percentage of U.S. postcards decreased to 30%. How many overseas postcards did he buy?

 71) If 60% of a number is 18, what is ½  % of the number?

 72) Denise and Peter shared some coins in the ratio of 11:5. If Denise received 30 more coins than Peter, how many coins were there all together?

 73) At the Costume Potluck, there were the same number of chocolate cupcakes as vanilla cupcakes. After 16 chocolate and 24 vanilla cupcakes had been eaten, the ratio of chocolate cupcakes to vanilla cupcakes was 11:9. How many cupcakes were brought to the Potluck lunch?

 74) Eight ninths of Ms. Diger’s students are in school today. Of those, ¾ remembered to bring in their homework. If 24 students forgot their homework, how many students does Ms. Diger have?

 75) Dave, Sue, Jill, and Fred shared a sum of money. Dave received 1/3 of the money, Sue received 1/6 of the money, Jill received ¼ of the money. There was $51 left for Fred. How much more money did Dave receive than Sue?

 76) In a bowl of M&Ms, Hazel found the number of orange M&Ms was 1/2 the number of brown M&Ms and the number of brown M&Ms was 1/3 the number of green M&Ms. If she counted 162 orange, brown, and green M&Ms altogether, how many brown ones were in the bowl?

 77) The ratio of the number of Jimmy’s marbles to the number of Kevin’s marbles is 3:4. After Jimmy bought another 60 marbles, he had twice as many marbles as Kevin. How many marbles did Jimmy have at first?

 78) Darren and Mick shared 96 marbles in the ratio 5:3. Darren then shared his marbles with Henry in the ratio 11:4. How many fewer marbles did Henry get than Mick?

 79) The ratio of the number of Ann’s picture cards to the number of Wendy’s picture cards was 7:8. After Wendy gave 8 picture cards to Ann, they each had the same number of picture cards. How many picture cards did they have altogether?

 80) The number of Paul’s toy soldiers and toy cars are in the ratio 3:4. If he throws away 1/3 of his toy soldiers and ½ of his toy cars, he will have 24 toy soldiers and toy cars left. How many toy soldiers and toy cars does he have altogether?

 81) Alvin’s monthly income is $1500. He spends part of this on food, rent, and transportation in the ratio 1:5:3. If he spends $200 less on transportation than on rent, how much money does he have left after spending on these three items?

 82) 10% of May’s beads are red, 35% of them are blue, and 50% of the remainder are yellow. If she has 6 more blue beads than yellow beads, how many more yellow beads than red beads does she have?

 83) At a sale, Dorothy bought a dress at a discount of 15% for $272 and a watch at a discount of 10% for $2700. How much did she save on the two sale items?

 84) 45% of the spectators at a stadium were men, 30% of them were women, 40% of the remainder were girls, and the rest were boys. If there were 120 more boys than girls, how many more men than women were there?

 85) The sum of two numbers is 110. The larger number is 2 less than 7 times the smaller. Find the larger number.

 86) Alice has 50% of the amount of money Betty has, and Carrie has 2/5 of what Alice has. If Betty has $364 more than Carrie, how much money does Alice have?

 87) A rectangular container 8 cm long and 9cm wide was filled with water to a depth of 6 cm. When 12 marbles of equal size were added to the container, the depth of the water became 7.5 cm. What is the volume of one marble?

 88) ½ of Andy’s money is 3/5 of Bob/s money. If Andy has $15 more than Bob, how much money do they have all together?

 89) The ratio of Zoe’s money to Yolanda’s is 3:7. Yolanda has $64 more than Zoe. If Yolanda gives ¼ of her money to Zoe, what will be the new ratio of Zoe’s money to Yolanda’s?

 90) In a jar filled with beads, 2/5 of the beads are blue, 1/3 of them are red, and the rest are green and yellow. The total number of red, green, and yellow beads is 126. There are ¾ as many green beads as yellow beads. How many yellow beads are there?

 91) Peter and Paul each had an equal amount of money. Each day Peter spent $36 and Paul spent $48. When Paul used up all his money, Peter still had $240 left. How much money did each of them have at first?

 92) Amanda spent 2/5 of her time after school doing homework and ¼ of her remaining time riding her bike. If she rode her bike for 45 minutes in a week, how much time did she devote to homework the same week?

 93) Mary bought 4 skirts and 15 shirts for $216 altogether. If each skirt cost three times as much as each shirt, how much more did each skirt cost than each shirt?

 94) The ratio of the amount of Robert’s money to that of Jasmine’s is 4:11. The ratio of the amount of Morgan’s money to that of Jasmine’s is 5:6. If Robert and Jasmine have $36 altogether, how much more money does Morgan have than Robert?

 95) Lenore uses 7/30 of her money on a mattress, 2/5 of it on a table and 1/3 of the remainder on a pair of glasses. If she spent $100 more on the mattress than on the pair of glasses, how much money did she spend on the mattress?

 96) Lisa and Charlene have 100 beads altogether. If Lisa gives 35 beads to Charlene, Charlene will have three times as many beads as Lisa. How many beads does Lisa have?

 97) One fifth of the fence posts around Wildwood park are oak, and the rest are pine. Justin places reflectors on 1/3 of the pine fence posts.  If 231 fence posts in Wildwood Park do not have reflectors, how many are oak?

 98) If Alex sells his computer for $2392, he makes a profit of 30%.What price should he charge if he wants a profit of 40%?

 99) Alvin’s monthly income is $1500. He spends part of this on food, rent, and transportation in the ratio 1:5:3. If he spends $200 less on transportation than on rent, how much money does he have left after spending on these three items?

 100) There were 600 children on a field. Thirty percent of them were boys. After 5 teams of boys joined the children on the field, the percentage of the children who were boys increased to 40%. How many boys were there in the 5 teams altogether?