Equation Word Problems

Show your work for each problem.

1.
Which equation represents: "A number increased by 7 equals 15"?
1. a)
2. b)
3. c)
4. d)
Answer:
"A number increased by 7" translates to . "Equals 15" means . Together: .
2.
"5 less than a number" is written as:
1. a)
2. b)
3. c)
4. d)
Answer:
"5 less than a number" means we start with the number and subtract 5. So . Remember: the number AFTER "than" comes first!
3.
A number plus 8 equals 20. What is the number?
Answer: 12
Equation: . Subtract 8 from both sides: .
4.
Three times a number is 27. What is the number?
Answer: 9
"Three times a number" is . So . Divide by 3: .
5.
Which phrase means ?
1. a)2 more than 5 times a number
2. b)Twice a number minus 5
3. c)5 more than twice a number
4. d)5 times a number plus 2
Answer: 5 more than twice a number
means: first double the number (), then add 5. That's "5 more than twice a number".
6.
Tom is 4 years older than his sister. Together, their ages add up to 24. How old is Tom?
Answer: 14
1. Let x = sister's age. Write Tom's age in terms of x: x + 4
2. Write the equation for their ages adding to 24: x + (x + 4) = 24
3. Simplify: What is ? 2x + 4
4. Solve . What is x (sister's age)? 10
5. Tom's age is . What is Tom's age? 14
7.
A number decreased by 9 equals 14. What is the number?
Answer: 23
. Add 9 to both sides: . Check: ✓
8.
A book costs 8 euros less than a game. Together they cost 42 euros. Which equation models this?
1. a)
2. b)
3. c)
4. d)
Answer:
Let x = game price. Book = x - 8 (8 less). Together: game + book = .
9.
A rectangle's length is 5 cm more than its width. The perimeter is 46 cm. Find the width.
Answer: 9
1. Let w = width. Express the length in terms of w: w + 5
2. Perimeter formula: . Write the equation: 2(w + 5) + 2w = 46
3. Expand and simplify. What do you get? 4w + 10 = 46
4. Solve for w: 9
10.
Movie tickets cost 12 euros for adults and 7 euros for children. A group bought 8 tickets and paid 76 euros total. How many adult tickets were purchased?
Answer: 4
1. Let a = adult tickets. Express child tickets in terms of a: 8 - a
2. Write the cost equation (adult cost + child cost = 76): 12a + 7(8 - a) = 76
3. Expand : 56 - 7a
4. Simplify : 5a + 56 = 76
5. Solve for a: 4
11.
Twice a number, decreased by 5, is 13. What is the equation?
1. a)
2. b)
3. c)
4. d)
Answer:
"Twice a number" = . "Decreased by 5" = subtract 5. So . Note: would be "twice (a number decreased by 5)" - different meaning!
12.
The sum of three consecutive integers is 72. What is the smallest integer?
Answer: 23
Let integers be x, x+1, x+2. Sum: . Simplify: , , .
13.
A train travels at 80 km/h. A car starts 2 hours later traveling at 120 km/h on the same route. After how many hours will the car catch up to the train?
Answer: 4
1. Let t = car's travel time in hours. How long has the train been traveling? t + 2
2. Write the train's distance (speed x time): 80(t + 2)
3. Write the car's distance: 120t
4. When they meet, distances are equal. Write the equation: 120t = 80(t + 2)
5. Solve: . What is t? 4
14.
A piggy bank contains coins worth 3.40 euros. There are 8 more 20-cent coins than 50-cent coins. How many 50-cent coins are there?
Answer: 4
1. Let x = number of 50-cent coins. Express 20-cent coins in terms of x: x + 8
2. Value of 50-cent coins in euros: 0.50x
3. Value of 20-cent coins in euros: 0.20(x + 8)
4. Total value equation: 0.50x + 0.20(x + 8) = 3.40
5. Simplify and solve for x: 4
15.
Ana has 3 times as many stickers as Ben. Together they have 48 stickers. How many does Ana have?
1. a)16
2. b)12
3. c)36
4. d)24
Answer: 36
Let x = Ben's stickers. Ana = 3x. Together: , so , . Ana has stickers.
16.
A phone plan costs 15 euros per month plus 0.05 euros per text message. If the monthly bill is 23 euros, how many text messages were sent?
Answer: 160
1. Let m = number of messages. Write the equation for total cost: 15 + 0.05m = 23
2. Subtract 15 from both sides: 0.05m = 8
3. Divide by 0.05: 160
17.
Half of a number is 9. What is the number?
Answer: 18
. Multiply both sides by 2: .
18.
The product of a number and 4, increased by 6, equals 30. What is the number?
1. a)8
2. b)9
3. c)6
4. d)5
Answer: 6
. Subtract 6: . Divide by 4: .