Hello from MrBillDoesMath
Answer: + 4/7, 6 (13/14)
Discussion:
Let L be the larger of the two numbers and S the smaller of the two. Then the first sentence translates into this:
-6L - L = -4 =>
-7L = -4 => (divide both sides by -7)
L = - (-4)/(-7) = + 4/7 (*)
The second sentence translates to
2 (L + S) = 15 => (divide both sides by 2)
(L +S) = 15/2 => (subtract L from each side)
S = 15/2 - L = 15/2 - 4/7 (using (*) above)
So
S = 15*7/(2*7) - (4*2)/(7*2) (combine over common denominator of 14)
S = 105/14 - 8/14 = 97/14 = 6 13/14
Something is crazy here! While 2(L +S) = 15 -- check it out -- our larger number L ( =4/7) is actually smaller than the S number (6 13/14)! Maybe I should have called them Y and X, respectively, as you suggested!
Thank you,
Mr. B
