Question

For three consecutive years, Sam invested some money at the start of the year. The first year, he invested x dollars. The second year, he invested $2,000 less than times the amount he invested the first year. The third year, he invested $1,000 more than of the amount he invested the first year. During the same three years, Sally also invested some money at the start of every year. The first year, she invested $1,000 less than times the amount Sam invested the first year. The second year, she invested $1,500 less than 2 times the amount Sam invested the first year. The third year, she invested $1,400 more than of the amount Sam invested the first year.
 If Sam and Sally invested the same total amount at the end of three years, the amount Sam invested the first year is $ ____ and the amount Sally invested the last year is $____ .

Answer 1

$\bf \stackrel{\textit{Sam invested the first year}}{x} \qquad \qquad \stackrel{\textit{2nd year is \ 2,000 less than \underline{x}}}{x-2000} \\\\\\ \stackrel{\textit{3rd year is \ 1,000 more than \underline{x}}}{x+1000}\qquad \qquad \boxed{\stackrel{\textit{Sam total investment}}{(x)+(x-2000)+(x+1000)}}\\\\ -------------------------------\\\\ \stackrel{\textit{Sally invested the first year \ 1000 less than \underline{x}}}{x-1000}$

$\bf \stackrel{\textit{2nd year is \ 1500 less than \underline{2x}}}{2x-15000}\qquad \qquad \stackrel{\textit{3rd year is \ 1400 more than \underline{x}}}{x+1400} \\\\\\ \boxed{\stackrel{\textit{Sally total investment}}{(x-1000)+(2x-1500)+(x+1400)}}$

$\bf \stackrel{\textit{Sam total investment}}{(x)+(x-2000)+(x+1000)}=\stackrel{\textit{Sally total investment}}{(x-1000)+(2x-1500)+(x+1400)} \\\\\\ 3x-1000=4x-1100\implies 100=x\impliedby \textit{Sam invested the first year} \\\\\\ \stackrel{\textit{Sally invested last year}}{x+1400}\implies 10+1400\implies 1500$