Question 1152558

One third the sum of two numbers is 50 and one fifth of their difference is 2. Find the numbers
<pre>Let the 1st and 2nd numbers be F and S, respectively
Then we get: {{{system(matrix(1,10, (1/3) * (F + S), "=", 50, "====>", F + S, "=", 150, "---", eq, "(i)"), matrix(1,10, (1/5) * (F - S), "=", 2, "=====>", F - S, "=", 10, "----", eq, "(ii)"))}}} 
2F = 160 ------ Adding eqs (i) & (ii)
F, or 1st number = {{{highlight_green(matrix(1,3, 160/2, "=", 80))}}}
80 + S = 150 ------ Substituting 80 for F in eq (i)
S, or 2nd number = {{{highlight_green(matrix(1,3, 150 - 80, "=", 70))}}}