Mathematics High School

The number x is a two-digit number.


• When x is divided by 9, the remainder is 1.


• When x is divided by 10, the remainder is 3.


What is the remainder when x is divided by 11?


Be sure to explain how you got your answer.

Answers

Answer 1

Answer:

x = 73

x ÷ 11 = 73 ÷ 11 = 6.636 or [tex]6\frac{7}{11}[/tex] or  ( 6 remainder 7)

Step-by-step explanation:

1. In order to determine the value of x, we will first find a two-digit multiple of 9 that has a unit value of (2)

Multiples of 9 = 18, 27, 36, 45, 54, 63, 72, 81, ...

from the above, the multiple of 9 that has a unit value of '2' is 72 ( 7 tens and 2 units)

2. Next, we will add 1 to the multiple of 9 found in step 1 above, to create a unit value of '3'. This is because when the number is divided by 9, we want to have a remainder of 1, and when the number is divided by 10, and we want to have a remainder of 3

72 + 1 = 73 ( 7 tens and 3 units)

3. Finally, let us divide the number in step 2 above by 10

73 ÷ 10 = 7 remainer 3.

Now the number 73 satisfies the three conditions given in the question:

1) The number x is a two-digit number.

73 is a two-digit number  

2) When x is divided by 9, the remainder is 1.

73 ÷ 9 = 8 remainder 1

3) When x is divided by 10, the remainder is 3.

73 ÷ 10 = 7 remainder 3

∴ x = 73

x ÷ 11 = 73 ÷ 11 = 6.636 or ( 6 remainder 7)

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Answers

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