Translating Words to Equations

Show your work for each problem.

1.
Which equation represents "a number increased by 5 equals 12"?
1. a)
2. b)
3. c)
4. d)
Answer:
"Increased by" means addition. A number () increased by 5 is , and this equals 12.
2.
What does "the product of 4 and a number" translate to?
1. a)
2. b)
3. c)
4. d)
Answer:
"Product" means multiplication. The product of 4 and a number is .
3.
Translate "5 less than " into an algebraic expression.
Answer: x - 5
"5 less than " means minus 5, written as . The phrase reverses the order: we subtract 5 FROM .
4.
Translate "the sum of and 8" into an algebraic expression.
Answer: x + 8
"Sum" means addition. The sum of and 8 is .
5.
What operation does the word "quotient" indicate?
1. a)Subtraction
2. b)Multiplication
3. c)Division
4. d)Addition
Answer: Division
"Quotient" is the result of dividing one number by another. For example, the quotient of 12 and 4 is .
6.
Translate "twice a number decreased by 7" into an algebraic expression.
Answer: 2x - 7
"Twice a number" is . "Decreased by 7" means subtract 7. So the expression is .
7.
Which equation represents "three times the sum of a number and 4 equals 21"?
1. a)
2. b)
3. c)
4. d)
Answer:
"The sum of a number and 4" is . We multiply this entire sum by 3: . This equals 21, so .
8.
Translate and solve: "A number multiplied by 4, then increased by 6, equals 30."
Answer: 6
1. What does "a number multiplied by 4" translate to? 4x
2. What does "increased by 6" do to the expression? 4x + 6
3. Write the complete equation: 4x + 6 = 30
4. Solve: Subtract 6 from both sides. What is 4x? 24
5. Divide by 4 to find x: 6
9.
Write an equation for: "8 more than triple a number is 29." Then solve.
Answer: 7
1. What is "triple a number"? 3x
2. What is "8 more than triple a number"? 3x + 8
3. Write the equation: 3x + 8 = 29
4. Subtract 8 from both sides: 3x = 21
5. Divide by 3 to find x: 7
10.
A shirt costs 12€ more than a hat. If the shirt costs 35€, write an equation for the hat's cost ().
Answer: h + 12 = 35
"12€ more than a hat" means hat + 12. The shirt costs 35€, so: . Solving: €.
11.
Maria's age is 3 years less than twice her sister's age. Maria is 15. How old is her sister?
Answer: 9
1. Let = sister's age. What is "twice her sister's age"? 2s
2. What is "3 years less than twice her sister's age"? 2s - 3
3. Maria is 15, so write the equation: 2s - 3 = 15
4. Add 3 to both sides: 2s = 18
5. Divide by 2 to find the sister's age: 9
12.
Which equation represents "the difference between a number and 7, divided by 2, equals 5"?
1. a)
2. b)
3. c)
4. d)
Answer:
"The difference between a number and 7" is . This entire expression is divided by 2: . This equals 5.
13.
A concert ticket costs 5€ more than half the cost of a VIP ticket. If a regular ticket costs 35€, what is the VIP ticket price?
Answer: 60
1. Let = VIP ticket price. What is "half the cost of a VIP ticket"? v/2
2. What is "5€ more than half the VIP ticket"? v/2 + 5
3. The regular ticket costs 35€. Write the equation: v/2 + 5 = 35
4. Subtract 5 from both sides: v/2 = 30
5. Multiply by 2 to find the VIP price: 60
14.
The perimeter of a rectangle is 48 cm. The length is 6 cm more than the width. Find the width.
Answer: 9
1. Let = width. What is the length in terms of ? w + 6
2. What is the perimeter formula? (P = 2l + 2w) 2(w+6) + 2w
3. Simplify: equals? 4w + 12
4. Set equal to 48 and solve for w. Subtract 12: 4w = 36
5. Divide by 4 to find the width: 9
15.
You earn 15€ per hour plus a 25€ bonus. Write an equation for total earnings () in terms of hours worked ().
Answer: E = 15h + 25
"15€ per hour" translates to . Adding the 25€ bonus: .
16.
The sum of three consecutive integers is 72. Find the smallest integer.
Answer: 23
1. Let = first integer. What is the second consecutive integer? n + 1
2. What is the third consecutive integer? n + 2
3. Write the sum of all three: n + (n+1) + (n+2)
4. Simplify and set equal to 72: 3n + 3 = 72
5. Solve for n: 23