Question

If the digits of a three-digit number are reversed in order, then the sum of the new resulting number and the original number comes out to be 665. The difference of the two numbers is 297. The tens’ digit place is two times the hundreds’ place digit. What is the number?

I know two equations are x+y=665 and x-y=297

Answer 1

@UnkleRhaukus

Answer 2

@horsegirl27

Answer 3

this is from con nexus
CHEATING IS BAD

Answer 4

You have two equations with two unknowns, which is sufficient to solve this problem:
$$
x+y=665\\
x-y=297
$$
Now solve
You can add these two equations
$$
x+y=665\\
x-y=297
$$
to get
$$
2x=665+297\\
$$
From which you can get x. Use this to solve for y
$$
y=665-x\\
$$
When you get your answer, the relationship between x and y and between the tens and hundreds place will be confirmed, but you don't need it to solve this problem because you have your two equations and two unknowns.

Conversely, if you did not have these two equations and only that relationship between the digits, you'd be able to come to the same conclusion. So in essence, the additional information regarding the digits is redundant.

Just remember, if you have two unknowns then you need two equations or two facts that relate the unknowns to each other.

Answer 5

CHEATING BAD