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

Answer:

64

Step-by-step 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

$a = \dfrac{15}{10}b=\dfrac{3}{2}b=\dfrac{3}{2}(10-a)=15-\dfrac{3}{2}a\\\\ \dfrac{2+3}{2}a = 15\\\\ 5a=30 a = 6$

and then, b = 10 - 6 = 4.

So the solution is 64.

Thank you