Question Bank: Finding the Unknown

If the weight of 3 apples is equal to the weight of 2 oranges, and the weight of one orange is 4 units, what is the weight of one apple?

If 2 weights x + 4 and x + 10 are equal, what is the value of x?

If Jane has 5 kg more than Tom and their combined weight is 35 kg, what is Tom's weight?

In a scale, 4 boxes weigh 16 kg combined while 2 boxes weigh as much as 1 box and 16 kg. What is the weight of one box?

What is the solution for y in the equation 3y + 6 = 24?

How many matchsticks are used in the arrangement at position 4?

You have two pans. One is filled with 5 kg of apples, and the other is 3 kg plus an unknown weight x. When equalized, the apples are equal to the weight of apples plus x. What is x?

What is the number of matchsticks in the arrangement at position 5?

If the scale reads 10 kg for two equal weights and 5 kg for one, what concept explains this situation?

What pattern do the matchstick arrangements follow?

If 2 pots weigh 4 kg and a pot weighs twice more than a kettle, what could be the weight of the kettle?

If Jasmine uses 99 matchsticks, what is the position number of her arrangement?

If 7 times the unknown weight is reduced by 5 and equals 12, what is the unknown weight?

How many matchsticks are in the arrangement at position 10?

If you remove 5 kg from a basket weighing 20 kg, what remains in the basket?

Can an arrangement be created using exactly 200 matchsticks?

Three cats weigh 6 kg, and when balanced, two cats equal one dog. What is the dog's weight if the cats weigh the same?

What would be the LHS of the equation for position 30?

If x + 12 = 5, what is the value of x?

Starting from the first position, how many additional matchsticks are needed to reach the 20th position?

If 15 sacks weigh together 120 kg and 10 are filled with the same weight, while 5 are empty, how much does one sack weigh?

What is the difference in the number of matchsticks between the 1st and 2nd positions?

If 4c = 64, find c.

If an arrangement at position n uses 51 matchsticks, what is the value of n?

Which method can ensure that both sides of the equation remain balanced?

What is the sum of the matchsticks used in position 3 and position 4?

What will be the number of matchsticks for arrangement at position 15?

How many matchsticks are needed for the arrangement at position 12?

By how many matchsticks does the arrangement at position 6 exceed that of position 5?

Can you create an arrangement using 100 sticks, based on the sequence formula?

If n is 10, how many matchsticks are used?

At position 8, how many matchsticks would there be?

What equation represents the weights on a scale with 3 slices of bread (2 each) and 2 fried eggs?

For the equation 4 + 2y = 16, what is the value of y?

If we denote the weight of 2 apples as a and it equals 10, what is a in the equation 2a = 10?

If 5x - 4 = 6, what is the value of x?

Frame an equation from the statement: 'a number divided by 4 equals 7.'

What equation would result if two friends save money, one starting with $400 and the other with $600, saving $50 per month?

If an equation sums 3 numbers x + y + z = 15, how can we isolate z?

From the weighing problem of 8 and y = 20, what equation can you derive?

Solve: 3x + 7 = 16. What is the value of x?

Frame an equation for: '3 less than 2 times a number equals 10.'

Solve for y in: 2y + 3 = 13.

If a number is multiplied by 3 then 5 is added, totaling 20, what is the equation?

What is the solution of 4z - 16 = 0?

Construct an equation for: 'twice a number decreased by 4 equals 10.'

From the scale, we have: 4 + 3x = 25. What is x?

What is the solution to the equation 2e = 6?

If 4 + 2y = 16, what is the value of y?

Solve for x in the equation 5x - 4 = 6.

What is the value of y in the equation 3y + 7 = 22?

Find n if 2n + 1 = 99.

What is the solution to the equation 6y + 7 = 25?

Solve for x in the equation 3x - 8 = 7.

If 7z - 11 = 3, what is the value of z?

What is the solution for m in the equation 4(m + 3) = 28?

Solve the equation 8x - 4 = 20.

In the equation 5x + 3 = 23, what is x?

What is the value of y in the equation 15 - 2y = 3?

Solve for a in the equation 6(a - 2) = 42.

If 3(y + 1) = 18, what is the value of y?

Solve for x in the equation 9x + 6 = 33.

If 12 = 3k - 6, what is the value of k?

If 16 = 2x + 4, what is x?

What is the solution of the equation 4x - 3 = 9?

Find the value of t in the equation 5(t + 2) = 45.

Solve for z in the equation 3z + 2 = 5.

What does the word 'bīja' mean in ancient Indian algebra?

Who is known as the key figure in the creation of algebra according to David Mumford?

What does the term 'al-jabr' translate to in English?

Which ancient Indian mathematician introduced systematic methods for solving equations?

What did ancient Indian mathematicians use to represent unknowns?

Brahmagupta's method for solving linear equations involved which main principle?

What denotes a known quantity in ancient Indian notation?

Which symbol was used for unknown variables in ancient Indian mathematics?

How was the equation '300 + 6x = 10x - 100' structured according to ancient practices?

Which famous mathematician translated Indian mathematical works into Arabic?

What was a common misconception about early algebraic notation?

Name the mathematical book written by Al-Khwarizmi that significantly influenced algebra.

What was the impact of translations of Indian mathematics in the 12th century?

In what way did Brahmagupta's work influence modern algebra?

If 4x + 6 = 10, what is the value of x? Identify any mistake in the solution.

In solving the equation 7 - 8z = 5, what mistake occurred in the steps?

For the equation 2v - 4 = 6, what was incorrect in the solution provided?

If 5z + 2 = 3z - 4, what is the correct solution for z?

Identify the error in solving 15w - 4w = 26.

What is the mistake in solving 3x + 1 = -12?

In solving the equation 4x - 5 = 9x + 8, identify the error.

If x + 9 = 66, how is x miscalculated?

In 4x = 2x + 8, what is the correct value of x?

If given 3x + 5 = 20, where is the mistake?

In solving 2x + 4 = 20, find the mistake in steps provided.

Identify the mistake in simplifying 28p - 36 = 98.

What is the outcome of 2x + 3 = 4x + 5?

How should one approach 5x + 4 = 2x + 8?