Solved Questions on Simple Equations
1. Solve the equation 2x + 9 = 19.
a) 2
b) 5
c) 7
d) 9
Answer: b) 5
Explanation: The given equation is 2x + 9 = 19
Transpose 9 to RHS
2x = 19 – 9
2x = 10
Now, divide both sides by 2
2x/2 = 10/2
x = 5
Hence, the solution of equation 2x + 9 = 19 is x = 5.
2. The sum of two consecutive even numbers is 86. Find the numbers.
a) 42 and 44
b) 34 and 52
c) 26 and 29
d) 22 and 26
Answer: a) 42 and 44
Explanation: Let us consider the consecutive even numbers as x and x + 2.
Given that the sum of two consecutive even numbers is 86.
x + (x + 2) = 86
x + x + 2 = 86
Transposing 2 from LHS to RHS, we get
2x = 86 – 2
2x = 84
Dividing both sides by 2 we get
2x/2 = 84/2
x = 42
Hence, the two consecutive numbers are 42 and 44.
3. Write the equation for the following statement. “The sum of four times a number and 5 gives a number five times it”.
a) 4x + 5 = 5
b) 4x + 5 = 1
c) 4x + 5 = 5x
d) 4 + 5x = 5
Answer: c) 4x + 5 = 5x
Explanation: Let the number be x.
Sum of 4x and 5 = 4x + 5
The sum is 5x.
The equation is 4x + 5 = 5x as required.
4. Solve the following equations: 3 (y – 2) = 2(y – 1) – 3
a) 0
b) 1
c) 2
d) 3
Answer: b) 1
Explanation: 3 (y – 2) = 2(y – 1) – 3
3y – 6 = 2y – 2 – 3 (Removing the brackets)
3y – 6 = 2y – 5
3y – 2y = 6 – 5 (Transposing 6 to RHS and 2y to LHS)
y = 1
Thus y = 1
5. If 5 is added to twice a number, the result is 29. Find the number.
a) 11
b) 12
c) 13
d) 14
Answer: b) 12
Explanation: Let the required number be x.
According to the question equation will be 2x + 5 = 29;
Solving the equation, we get
2x + 5 = 29
2x = 29 – 5 (Transposing 5 to RHS)
2x = 24
x = 12 (Dividing both sides by 2)
x = 12
Thus, the required number is 12.
Practice Questions on Simple Equations
1. If one-third of a number exceeds its one-fourth by 1, find the number.
a) 11
b) 12
c) 13
d) 14
Answer: b) 12
2. Seven times a number is 12 less than thirteen times the same number. Find the number.
a) 1
b) 2
c) 3
d) 4
Answer: b) 2
3. Write the following statement in the form of an equation. ‘One-fourth of a number is 2 more than 5’.
a) (1/4) x = 7
b) 4x = 1/7
c) 1/2x = 2/5
d) 4x = 11
Answer: a) (1/4) x = 7
4. Solve the following equation. (5z+1)/3 = 7
a) 2
b) 5
c) 4
d) 11
Answer: c) 4
5. Solve the following equation. 16 = 4 + 3 (t + 2)
a) 1
b) 2
c) 3
d) 4
Answer: b) 2
6. The difference between the two numbers is 12. The ratio of the two numbers is 5:3. What are the two numbers?
a) 30 and 18
b) 39 and 27
c) 48 and 36
d) 40 and 28
Answer: a) 30 and 18
7. The cost of two tables and three chairs is $780. If the table costs $40 more than the chair, find the cost of the table and the chair.
a) $50 and $90
b) $100 and $140
c) $150 and $190
d) $180 and $140
Answer: d) $180 and $140
8. Soniya’s father is 4 times as old as Soniya. After 5 years, father will be three times as old as Soniya. Find their present ages.
a) 20 and 80
b) 10 and 40
c) 12 and 48
d) 11 and 44
Answer: b) 10 and 40
9. Using the equation, find the value of b. 19 − 3(b−7) = b + 2(b + 5)
a) 20
b) 12
c) 16
d) 5
Answer: d) 5
10. Solve for z: 3(5z + 3) = 2(7z+8)
a) 5
b) 7
c) 6
d) 8
Answer: b) 7
