How to Approach Word Problems

Show your work for each problem.

1.
What is the FIRST step in the UPSC strategy for solving word problems?
1. a)Solve step by step
2. b)Understand the problem
3. c)Plan your approach
4. d)Check your answer
Answer: Understand the problem
The first step is always to UNDERSTAND the problem. You need to know what information you have and what you're looking for before you can plan how to solve it.
2.
Which key word usually tells you to ADD?
1. a)Remaining
2. b)Divided equally
3. c)Each
4. d)In total
Answer: In total
'In total' usually means you need to add numbers together to find the combined amount. 'Remaining' suggests subtraction, 'each' often means multiply or divide, and 'divided equally' means division.
3.
Sam has 15 marbles. He gives 6 to his friend. How many marbles does Sam have now?
Answer: 9
Sam gives away marbles, so we subtract: marbles.
4.
A bakery made 24 cookies in the morning and 18 cookies in the afternoon. How many cookies did they make in total?
Answer: 42
The word 'total' tells us to add: cookies.
5.
Why is it important to CHECK your answer after solving a word problem?
1. a)To make the problem look harder
2. b)To waste time
3. c)Because the teacher told you to
4. d)To make sure the answer is reasonable and answers the question
Answer: To make sure the answer is reasonable and answers the question
Checking helps you catch calculation errors and make sure your answer makes sense in the context of the story. An answer like 'negative 5 apples' would tell you something went wrong!
6.
There are 32 students in a class. 8 students are absent today. The remaining students are divided into 4 equal groups. How many students are in each group?
Answer: 6
Step 1: Find students present: students. Step 2: Divide into groups: students per group.
7.
A store has 50 apples. In the morning, they sell 15 apples. In the afternoon, they receive 20 more apples. How many apples does the store have now?
1. a)45
2. b)55
3. c)35
4. d)85
Answer: 55
Start with 50, subtract 15 (sell), then add 20 (receive): apples.
8.
Lisa has 36 stickers. She wants to share them equally among her 4 friends and keep the same amount for herself. How many stickers does each person get?
Answer: 7
1. How many people will share the stickers in total (including Lisa)? 5
2. What operation do we use to share equally? division
3. Calculate: 7
9.
A bookstore has 72 books. They put 8 books on each shelf. How many shelves do they need?
Answer: 9
1. What is the total number of books? 72
2. How many books go on each shelf? 8
3. What operation finds how many groups of 8 fit into 72? division
4. Calculate: 9
10.
Tom has some money. He spends 12 dollars on lunch and has 23 dollars left. Which expression shows how to find how much money Tom started with?
1. a)
2. b)
3. c)
4. d)
Answer:
Tom spent 12 and has 23 left. To find what he started with, we add what he spent to what he has left: dollars.
11.
A farmer has 120 eggs. He sells 48 eggs at the market and then his chickens lay 36 more eggs. He packs the remaining eggs into cartons of 12. How many full cartons can he make?
Answer: 9
1. How many eggs does the farmer have after selling 48? 72
2. How many eggs does he have after the chickens lay 36 more? 108
3. How many eggs go in each carton? 12
4. How many full cartons: 9
12.
A cinema has 156 seats arranged in 12 equal rows. The first 5 rows are filled with students, and 18 more people sit in the remaining rows. How many empty seats are there?
Answer: 73
Seats per row: . Students in first 5 rows: . Total occupied: . Empty seats: .
13.
Maria buys 3 notebooks at 4 dollars each and 2 pens at 3 dollars each. She pays with a 20 dollar bill. How much change does she receive?
Answer: 2
1. How much do 3 notebooks cost? () 12
2. How much do 2 pens cost? () 6
3. What is the total cost? 18
4. How much change from 20 dollars? 2
14.
A bus can carry 45 passengers. On Monday, it makes 4 trips with full passengers. On Tuesday, it makes 3 trips but carries only 38 passengers per trip. How many more passengers did it carry on Monday than Tuesday?
Answer: 66
1. How many passengers on Monday? (4 full trips) 180
2. How many passengers on Tuesday? (3 trips with 38 each) 114
3. How many MORE on Monday than Tuesday? 66
15.
A school is planning a field trip. There are 126 students going. Each bus holds 28 students. Buses cost 150 dollars each. What is the total cost for buses?
Answer: 750
1. How many buses are needed for 126 students if each bus holds 28? 5
2. What is the cost per bus? 150
3. What is the total cost? (buses times cost per bus) 750