Question

a two-digit number is 21 times the difference

Answer 1

Answer:

This statement can be written as:

10x + y = 21(x - y)

Step-by-step explanation:

This statement can be written as

10x + y = 21 (x - y)

10x + y = 21x - 21y

11x = 22y

x = 2y

If y = 1, then x = 2

if 21 is the two-digit number, then that is equal to 21 times the difference between 2 and 1.

Likewise, if y = 2, then x = 4

if 42 is the two-digit number, then that is equal to 21 times the difference between 4 and 2.

if y = 1000, then x = 2000, if the two-digit is 21000, then that is equal to 21 times the difference between 2000 and 1000.

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Answer 2

Answer:

21, 42, 63, 84

Step-by-step explanation:

Let the two digits of the two-digit number be represented by 'x' in the Tens place and 'y' in the Units place.

∴ The two-digit value will be 10x+y

Now the difference means (x-y) or it can mean (y-x) also, but it will not have changes in the answer. So, I will take (x-y) as the difference.

∴ 10x+y=21(x-y)

10x+y=21x-21y

y+21y=21x-10x

22y=11x

2y=x

∴ 2y=x

or x=2y

Since it is a two-digit number, it means that x≠0

∴ y≠0

and also y≠5 as this would give us x=10

Hence we are left with the values of 1, 2, 3, and 4 for y

So, the possible numbers can be

21, 42, 63, 84

Check

(i) 21

12-1=1

21=21×1

(ii) 42

4-2=2

42=21×2

(iii) 63

6-3=3

63=21×3

(iv) 84

8-4=4

84=21×4