Marble and Toy Production Problems

The video tutorial covers six algebraic problems involving marbles, toy production, sum and product of numbers, consecutive integers, right triangle dimensions, and potter articles. Each problem is solved using algebraic equations, demonstrating methods to find unknown values based on given conditions.

If John and Janti together have 45 marbles and both lose 5 marbles each, what is the product of the number of marbles they now have?

• 200

• 150

• 100

• 124

What is the initial number of marbles John had if the product of the remaining marbles is 124?

• 9

• 45

• 36

• 5

In a toy production problem, if the cost of production per toy is 55 minus the number of toys produced, what is the total cost if 30 toys are produced?

• 750

• 1000

• 900

• 600

How many toys were produced if the total production cost was 750 rupees?

• 20

• 30

• 15

• 25

Find two numbers whose sum is 27 and product is 182.

• 12 and 15

• 13 and 14

• 10 and 17

• 9 and 18

What is the sum of two numbers if their product is 182?

• 30

• 27

• 20

• 25

Find two consecutive positive integers whose squares sum up to 365.

• 12 and 13

• 14 and 15

• 15 and 16

• 13 and 14

What is the sum of the squares of two consecutive integers if one of them is 13?

• 300

• 350

• 400

• 365

In a right triangle, if the altitude is 7 cm less than the base and the hypotenuse is 13 cm, what is the length of the base?

• 10 cm

• 12 cm

• 14 cm

• 15 cm

What is the altitude of a right triangle if the base is 12 cm and the hypotenuse is 13 cm?

• 7 cm

• 6 cm

• 8 cm

• 5 cm