Question

One number is 10 more than another. The sum of twice the smaller plus three times the larger, is 55. What are the two numbers?

Answer 1

If we take the numbers to be hmm say "a" and "b"
let's say "a" is the bigger number, how big?

well "One number is 10 more than another"
so... whatever "b" is, "a" is THAT plus 10, or
a = b+ 10

now, how much is twice the smaller? the smaller is b
twice b, is 2 * b or 2b

what about three times the larger? the larger is a
thrice a is 3 * a or 3a

we're told that 2b + 3a = 55
thus$\bf \begin{cases} a=b+10 \\\\ 2b+3a=55\\ --------------\\ 2b+3\left( \boxed{b+10} \right)=55 \end{cases}$

solve for "b", to see what the smaller one is

what about "a"? well, a = b + 10