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Sum and product of digits problem
By jitender singh on Wednesday, November 3, 1999 - 01:08 am:

Please help me solve the following algebra problem.

Problem: A two-digit number is four times the sum and three times the product of its digits. Find this number.

By Anton Ilderton (Abi20) on Wednesday, November 3, 1999 - 02:25 am:

Dear Jitender,

The trick to solving this is to write the number as 10a + b where 1 < a < 9 and 0 < b < 9. This will give you a 2 digit number.

So, from the information you give, we have two equations:

10a + b = 3ab
10a + b = 4a + 4b

It's pretty straight forward to solve these equations (but if you've not got much experience with algebra then tell me and I'll post the full solution), and as far as I can see there is only one answer.

One hint: if you're doing things right, you'll find that a = b = 0 solves the equations, but this isn't strictly a solution since 0 isn't a 2-digit number.

Regards,
Anton.