what is a numbers cross sum?

Question

I have the following problem

A Three digit natural number's cross sum amounts to $14.$ When you read the number from right to left and subtract $22$, you obtain double the original number. Also the middle digit is equal to the sum of the outer two digits. Find the number

I am not sure what a cross sum is, and have been unable to find resources on it. We have been learning about matrices and know what a cross product is... but not a cross sum.

Answer 1

You have the following equations (under the restriction of $0\leq{a,b,c}\leq9$):

• $a+b+c=14$
• $100c+10b+a-22=2(100a+10b+c)$
• $b=a+c$

This is a system of $3$ equations in $3$ variables, which should be easy to solve:

• $a=2$
• $b=7$
• $c=5$

Hence the number is $275$.