How to approach this problem please?

[johnt55]

This is a missing numbers problem - what is the step by step process for solving these two problems please? There are two questions and answers.

Give ? numeric values 0 to 9 (each ? does not have to be the same value):
40? - ?25 = X

Q1. So that X is the largest number possible which is divisible by 3.
Q2. So that X is the smallest even number possible.

Help much appreciated.

Thank you.

 

[hoosie]

Try 409 - 125 = 284 (not divisible by 3 since digits add to 14 - not in 3 times table)
Next try 407 - 125 = 282 (divisible by 3 since digits add to 12 - in 3 times table)
Then try 409 - 025 = 384 (divisible by 3 since digits add to 15 - in 3 times table )
So highest value (9) and lowest value (0) gives highest number (384) divisible by 3

 

[Ishuda]

This is a missing numbers problem - what is the step by step process for solving these two problems please? There are two questions and answers.

Give ? numeric values 0 to 9 (each ? does not have to be the same value):
40? - ?25 = X

Q1. So that X is the largest number possible which is divisible by 3.
Q2. So that X is the smallest even number possible.

Help much appreciated.

Thank you.

To restate: given n, m, and X belonging to the Natural non-negative numbers with
X = 40 n - 25 m; \(\displaystyle n,m \le\, 9\).
X is divisible by 3.
Q1. What is the largest possible X?
Q2. What is the smallest possible X > 0?

What are your thoughts? What have you done so far? Please show us your work even if you feel that it is wrong so we may try to help you. You might also read
http://www.freemathhelp.com/forum/threads/78006-Read-Before-Posting

Hint: 40 = 24 + 15 + 1