Question 290166
The sum of two numbers is 32; the larger number is 12 greater than twice the smaller.  What are the 2 numbers?


Let the larger number be L, and the smaller S


Then L + S = 32 (their sum is 32)


Also, L = 2S + 12 (given that the larger, or L is 12 greater than twice the smaller, or S)


We now have:


L + S = 32 ------(i)

L - 2S = 12 ----- (ii)


Subtract eq (ii) from eq (i) to get: 3S = 20


Therefore, S =  {{{20/3}}}


Substitute this value for S in eq (i) to get: {{{L + (20)/3 = 32}}}


L = {{{32 - (20)/3}}} or {{{(76)/3}}}


Therefore, L, or the larger number is {{{highlight_green(76/3)}}}, while S, or the smaller number is: {{{highlight_green(20/3)}}}.