Question

Could anyone help me understand this? Thanks!

Answer 1

let's take a peek at some consecutive integers

2, 3, 4, 5, 6, 7, 8, 9 ......

notice, the integers are just 1 hop away from each other, 3-1 = 2, 3+1 = 4, and 2 and 3 and 4 are consecutive.

that means if we had an integer say "a", and we'd like to find a consecutive integer, or an integer next to it, we can find it by simply a ± 1, so hmm let's use say a + 1 for the next integer.

`\bf \stackrel{\textit{4 times the greater integer}}{4(a+1)}~\hspace{10em}\stackrel{\textit{3 times the lesser integer}}{3a} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{\textit{4 times the greater integer}}{4(a+1)}~~\stackrel{is}{=}~~\stackrel{\textit{3 times the lesser integer, and 18 more}}{3a+18} \\\\\\ 4a+4=3a+18\implies 4a-3a=18-4\implies \boxed{a=14}~\hspace{5em} \stackrel{a+1}{\boxed{15}}`