WRITING EQUATIONS WORKSHEET

Questions 1-8 : Translate each sentence into an equation.

Question 1 :

Eighteen more than a number is 125.

Question 2 :

Twenty is 7 less than twice a number.

Question 3 :

Nine less than twice a number is three more than the same number.

Question 4 :

Twice a number increased by fourteen is identical to fifty.

Question 5 :

Half the sum of seven and a number is the same as the number decreased by two.

Question 6 :

The quotient of m and n equals four more than one-third the sum of m and n.

Question 7 :

The quotient of p and q is twelve less than three times the sum of p and q.

Question 8 :

The cube of x plus the square of y is equal to fifty two.

Questions 9-12 : Write an equation to represent the given relationship between integers.

Question 9 :

The sum of four consecutive integers is -54.

Question 10 :

The product of three consecutive odd integers is 693.

Question 11 :

8 less than the sum of two consecutive integers is equal to 55.

Question 12 :

5 more than the product of two consecutive integers is equal to 25.

Questions 1-8 : Translate each sentence into an equation.

1. Answer :

Eighteen more than a number is 125

Let x be the number.

Equation :

x + 18 = 125

2. Answer :

Twenty is 7 less than twice a number

Let y be the number.

Equation :

20 = y - 7

3. Answer :

Nine less than twice a number is three more than the same number

Let n be the number.

Equation :

2n - 9 = n + 3

4. Answer :

Twice a number increased by fourteen is identical to fifty

Let x be the number.

Equation :

2x + 14 = 15

5. Answer :

Half the sum of seven and a number is the same as the number decreased by two

Let y be the number.

Equation :

(1/2)(7 + y) = y - 2

6. Answer :

The quotient of m and n equals four more than one-third the sum of m and n

Equation :

m/n = (1/3)(m + n) + 4

7. Answer :

The quotient of p and q is twelve less than three times the sum of p and q

Equation :

p/q = 3(p + q) - 12

8. Answer :

The cube of x plus the square of y is equal to fifty two

Equation :

x³ + y² = 52

9. Answer :

The sum of four consecutive integers is -54

Let x be the first integer.

Then, the remaining three integers are

x + 1, x + 2 and x + 3

Equation :

x + (x + 1) + (x + 2) + (x + 3) = -54

10. Answer :

The product of three consecutive odd integers is 693

Let y be the first integer.

Then, the remaining two integers are

y + 2 and y + 4

Equation :

y(y + 2)(y + 4) = 693

11. Answer :

8 less than the sum of two consecutive integers is equal to 55

Let x be the first integer.

Then, the second integer is x + 1.

Equation :

x + (x + 1) - 8 = 55

12. Answer :

5 more than the product of two consecutive integers is equal to 25

Let y be the first integer.

Then, the second integer is y + 1.

Equation :

y(y + 1) + 5 = 25

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