Integer Properties and Equations

The video tutorial guides viewers through solving a mathematical problem involving an integer between 10 and 100. The integer's value is eight times the sum of its digits, and reversing its digits reduces it by 45. The teacher breaks down the problem, explains place value, formulates equations, and solves them using substitution. The solution is verified to ensure it meets the problem's conditions.

What is the range of the integer discussed in the problem?

• Between 100 and 200

• Between 1 and 50

• Between 10 and 100

• Between 50 and 150

What does the term 'integer' refer to in the context of this problem?

• A whole number

• A decimal number

• A negative number

• A fraction

How is the number 31 represented using place value?

• 31

• 3 * 1 + 10

• 3 * 10 + 1

• 3 + 1

What is the first equation derived from the problem's conditions?

• 10a + b = 8(a + b)

• a + b = 10a + b

• 10a + b = a - b

• a = 8b

What happens to the integer when its digits are reversed?

• It doubles

• It decreases by 45

• It increases by 45

• It remains the same

What is the second equation derived from reversing the digits?

• 10b + a = 10a + b

• 10b + a = 45

• 10b + a = 10a + b - 45

• 10b + a = 10a + b + 45

Which method is used to solve the equations?

• Substitution method

• Trial and error

• Matrix method

• Graphical method

What is the final integer that satisfies the problem's conditions?

• 27

• 54

• 72

• 45

What is the sum of the digits of the final integer?

• 7

• 8

• 6

• 9

What is the product of the sum of the digits and 8 for the final integer?

• 64

• 72

• 90

• 81