Question

the sum of a two digit number is 10. the value of the number is 16 times the units digit. find the number

Answer 1

64

Explanation:

Hello, we can write this two digit number 'ab', a and b being positive integer between 0 and 9.

For instance , 54, a = 5 and b =4

The number can be written 10*a+b (54=5*10+4, for instance)

The sum of a two digit number is 10.

a + b = 10

The value of the number is 16 times the units digit.

10a + b = 16b <=> 10a = 16b - b = 15b

`<=> a = (15)/(10)b=(3)/(2)b=(3)/(2)(10-a)=15-(3)/(2)a\\\\<=> (2+3)/(2)a = 15\\\\<=> 5a=30 <=> a = 6`

and then, b = 10 - 6 = 4.

So the solution is 64.

Thank you