Question

Please help, I can't figure out how to set this up. There's supposed to be 2 equations.

Negative 6 times the larger of two numbers minus the larger is -4. Two times the sum of the numbers us 15. Find the numbers

Ps. Larger=Y
Smaller=X

Answer 1

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