Algebra Questions

Algebra is the basis for calculus, geometry, trigonometry, and statistics. The students of class 6, 7, 8, and 9 need to improve their understanding of algebraic principles. This would require practicing as many Questions as possible. These algebra Questions should cover a range of topics, including linear equations, quadratic equations, polynomials, etc.

In this article, we have provided you with a list of Questions on Algebra. Solving these Questions will help you understand the concepts thoroughly and easily.

Algebra Questions with Solutions

Following are some of the algebra questions along with their solutions:

Question 1: If there are 2 apples in a bag and x apples are added to it, making a total of 10 apples, how many apples were added?

Solution:

Let the number of apples added be x.

The total number of apples is 2 (initial) + x (added) = 10.

So, 2 + x = 10.

Subtract 2 from both sides to find x: x = 10 – 2.

Therefore, x = 8 apples were added.

Question 2: A pen costs x dollars. If 5 pens cost $15, what is the cost of one pen?

Solution:

Let the cost of one pen be x dollars.

The total cost for 5 pens is 5x = $15.

Divide both sides by 5 to find the cost per pen: x = 15 / 5.

Therefore, each pen costs $3.

Question 3: A train travels x miles in 2 hours. If it traveled 100 miles, how many miles does it travel in one hour?

Solution:

Let the distance traveled in one hour be x miles.

In 2 hours, the train travels 2x miles.

We know 2x = 100 miles.

Divide both sides by 2 to find x: x = 100 / 2.

Therefore, the train travels 50 miles in one hour.

Question 4: If x people can complete a task in 4 hours, and 8 people can complete the same task in 2 hours, how many people were originally there?

Solution:

Let the original number of people be x.

The work done is the same, so x people in 4 hours is equal to 8 people in 2 hours.

So, 4x = 2 * 8.

Simplify to find x: x = (2 * 8) / 4.

Therefore, x = 4 people were originally there.

Question 5: A rectangle’s length is twice its width. If the width is x feet and the area is 50 square feet, what is the width of the rectangle?

Solution:

Let the width be x feet.

The length is 2x feet.

The area of the rectangle is length * width, so 2x * x = 50.

Simplify to find x: x² = 50 / 2.

Solving for x, we get x = sqrt(25) = 5 feet.

Question 6: Sarah has x dollars. After buying a book for $10, she has $30 left. How much money did Sarah have initially?

Solution:

Let Sarah’s initial amount of money be x dollars.

After spending $10, she has x – 10 dollars left.

We know x – 10 = $30.

Add 10 to both sides to find x: x = 30 + 10.

Therefore, Sarah initially had $40.

Question 7: A school has x students in each class. If there are 5 classes and a total of 150 students, how many students are in each class?

Solution:

Let the number of students in each class be x.

Total students in 5 classes is 5x.

We know 5x = 150.

Divide both sides by 5 to find x: x = 150 / 5.

Therefore, there are 30 students in each class.

Question 8: A baker makes x cookies from a batch of dough. If he makes 120 cookies and divides them into 6 boxes, how many cookies are in each box?

Solution:

Let the number of cookies in each box be x.

The total number of cookies is 6x.

We know 6x = 120.

Divide both sides by 6 to find x: x = 120 / 6.

Therefore, each box contains 20 cookies.

Question 9: A baker used x cups of flour to make 3 cakes. If he used 15 cups in total, how many cups did he use for each cake?

Solution:

Let the cups of flour used for each cake be x.

The total flour used for 3 cakes is 3x cups.

So, 3x = 15.

Dividing both sides by 3, we get x = 15 / 3.

Therefore, x = 5 cups of flour per cake.

Question 10: In a garden, there are x roses and twice as many tulips. If there are 30 flowers in total, how many roses are there?

Solution:

Let the number of roses be x.

Then, the number of tulips is 2x.

The total number of flowers is x (roses) + 2x (tulips) = 30.

So, 3x = 30.

Dividing both sides by 3, x = 30 / 3.

Therefore, there are x = 10 roses.

Question 11: A car travels x kilometers in 1 hour. If it traveled 240 kilometers in 4 hours, what is its speed in kilometers per hour?

Solution:

Let the speed of the car be x kilometers per hour.

In 4 hours, the car travels 4x kilometers.

We know 4x = 240.

Dividing both sides by 4, x = 240 / 4.

So, the speed of the car is 60 kilometers per hour.

Question 12: A bottle contains x liters of water. After pouring out half of the water, 2 liters remain. How many liters were there initially?

Solution:

Let the initial amount of water be x liters.

Half of this amount is x / 2.

We know x / 2 = 2 liters.

Multiplying both sides by 2, x = 2 * 2.

Therefore, the bottle initially had 4 liters of water.

Question 13: In a class, there are x students. If 3 more students join the class, the total becomes 25. How many students were there initially?

Solution:

Let the initial number of students be x.

After 3 students join, the total is x + 3.

We know x + 3 = 25.

Subtracting 3 from both sides, x = 25 – 3.

So, there were initially 22 students in the class.

Question 14: A rectangle’s length is twice its width w. If the rectangle’s perimeter is 30 meters, what is its width?

Solution:

Let the width of the rectangle be w meters.

Its length is 2w meters.

The perimeter is 2(length + width) = 30.

Substituting length and width, we get 2(2w + w) = 30.

Simplifying, 6w = 30.

Dividing both sides by 6, w = 30 / 6.

So, the width of the rectangle is 5 meters.

Question 15: A pool is filled by x liters of water each minute. If it takes 10 minutes to fill 300 liters, how much water is filled each minute?

Solution:

Let the amount of water filled each minute be x liters.

In 10 minutes, the total filled is 10x liters.

We know 10x = 300.

Dividing both sides by 10, x = 300 / 10.

So, 30 liters of water is filled each minute.

Question 16: A store sells x apples in a day. If it sold 120 apples in 4 days, how many apples does it sell each day?

Solution:

Let the number of apples sold each day be x.

In 4 days, the total sold is 4x apples.

We know 4x = 120.

Dividing both sides by 4, x = 120 / 4.

Therefore, the store sells 30 apples each day.

Question 17: A train is x meters long and passes a pole in 3 seconds. If it passes the pole at a speed of 10 meters per second, how long is the train?

Solution:

Let the length of the train be x meters.

Speed = Distance / Time, so 10 = x / 3.

Multiplying both sides by 3, x = 10 * 3.

Therefore, the train is 30 meters long.

Question 18: A farmer has x chickens and 4 times as many cows. If he has a total of 100 animals, how many chickens does he have?

Solution:

Let the number of chickens be x.

The number of cows is 4x.

The total number of animals is x (chickens) + 4x (cows) = 100.

So, 5x = 100.

Dividing both sides by 5, x = 100 / 5.

Thus, there are 20 chickens.

Question 19: In the expression 7x³ – 4x² + 9x – 5, what is the coefficient of x²?

Solution:

Identify the term that contains x². The term is -4x².

The coefficient of x² is the number in front of the x² term, which is -4.

Question 20: Find the coefficient of x in the polynomial 3x⁴ – 2x³ + 5x – 7.

Solution:

Look for the term with x (to the first power). The term is 5x.

The coefficient of x is the number in front of the x term, which is 5.

Question 21: What is the coefficient of the constant term in the expression 8x² – 6x + 4?

Solution:

The constant term is the term without any variable, which is 4 in this case.

The coefficient of the constant term is the number itself, so it is 4.

Question 22: Simplify 3x + 5x.

Solution:

Combine the like terms by adding the coefficients.

3x + 5x becomes (3 + 5)x.

Therefore, the simplified expression is 8x.

Question 23: Find the result of 7y – 3y.

Solution:

Subtract the coefficients of the like terms.

7y – 3y becomes (7 – 3)y.

Thus, the result is 4y.

Question 24: Simplify 4a + 7b – 3a.

Solution:

Combine the like terms 4a and -3a.

4a – 3a becomes (4 – 3)a.

The expression simplifies to a + 7b.

Question 25: Calculate the sum of 5x + 8y and 3x – 2y.

Solution:

Add the like terms separately.

Combine 5x and 3x to get 8x.

Combine 8y and -2y to get 6y.

The result is 8x + 6y.

Question 26: What is the result of subtracting 2x – 3y from 6x + 4y?

Solution:

Subtract each term separately.

6x – 2x results in 4x.

4y – (-3y) becomes 4y + 3y, resulting in 7y.

The answer is 4x + 7y.

Question 27: Simplify the expression 9m – 5n + 2m + 3n.

Solution:

Combine like terms 9m and 2m to get 11m.

Combine -5n and 3n to get -2n.

The simplified expression is 11m – 2n.

Question 28: Find the sum of 3p + 4q and -2p – 6q.

Solution:

Add the like terms separately.

3p + (-2p) results in p.

4q + (-6q) results in -2q.

The final expression is p – 2q.

Question 29: Simplify the expression 4x² + 5x – 3 + 2x² – 7x + 6.

Solution:

Combine like terms.

Add 4x² and 2x² to get 6x².

Combine 5x and -7x to get -2x.

Add -3 and 6 to get 3.

The simplified expression is 6x² – 2x + 3.

Question 30: Find the result of subtracting 3y² – 4y + 7 from 5y² + 2y – 1.

Solution:

Subtract each term separately.

5y² – 3y² results in 2y².

2y – (-4y) becomes 2y + 4y, resulting in 6y.

-1 – 7 becomes -8.

The answer is 2y² + 6y – 8.

Question 31: Simplify the sum of 2x³ – 3x² + x – 5 and -x³ + 4x² – 2x + 6.

Solution:

Combine like terms.

Add 2x³ and -x³ to get x³.

Combine -3x² and 4x² to get x².

Add x and -2x to get -x.

Combine -5 and 6 to get 1.

The final expression is x³ + x² – x + 1.

Question 32: Give an expression for the following case:

The total cost (C) when buying x number of notebooks, each costing $3, and y number of pens, each costing $1.50.

Solution:

The cost for notebooks is $3 per notebook, so the cost for x notebooks is 3x.

The cost for pens is $1.50 per pen, so the cost for y pens is 1.50y.

The total cost, C, is the sum of these costs: C = 3x + 1.50y.

Question 33: Give an expression for the following case:

The perimeter (P) of a rectangle with a length of (2x + 5) meters and a width of (x + 3) meters.

Solution:

The perimeter of a rectangle is given by P = 2(length + width).

Substituting the given lengths, P = 2((2x + 5) + (x + 3)).

Simplifying, P = 2(3x + 8).

Question 34: Give an expression for the following case:

The area (A) of a triangle with a base of (x + 4) meters and a height of (2x – 3) meters.

Solution:

The area of a triangle is given by A = 1/2(base * height).

Substituting the given measurements, A = 1/2((x + 4) * (2x – 3)).

Simplifying, A = (x + 4)(x – 1.5).

Question 35: Give an expression for the following case:

The total distance (D) traveled when driving x kilometers at a speed of 60 km/hr and then an additional y kilometers at 80 km/hr.

Solution:

The distance does not depend on the speed, so the total distance is simply the sum of the two individual distances.

Therefore, D = x + y.

Related Links:

Algebraic Formulas

Algebraic Expressions

Polynomials