Find the number.

Question

A two-digit no. is 3 more than 4 times the sum of its digits.. If 18 is added to the the no. its digits are reversed. Find the number.

Answer 1

Remember the drill back in grade school? Example: 156 = 100 + 50 + 6 or you can write that as 156 = 100*1 + 10*5 + 1*6. That's the thought when solving for digit problems. The multiplier 1,10,100 and so on are fixed.

 

A two-digit no. is 3 more than 4 times the sum of its digits.

 

Let:

t = tens, u = ones

 

The two-digit number would be (10t + u), as shown in the example above. It would be 3 more than 4 times the sum of digits, which is simply (t+u):

 

(10t + u) = 4(t+u) + 3

 

Simplifying,

 

10t + u = 4t + 4u + 3

 

6t - 3u = 3        eq. 1

 

If 18 is added to the number, its digits are reversed. To do the reverse representation, just reverse the multipliers. The reverse number would be (10u + t):

 

(10t + u) + 18 = 10u + t

 

9t - 9u = -18     eq. 2

 

Two equations, two unknown, you could do elimination or substitution:

 

3[6t - 3u = 3]3

 

18t - 9u = 9

9t - 9u = -18

9t = 27

 

t = 3

 

9(3) - 9u = -18

-9u = -45

 

u = 5

 

The number is 35.