# The Sum Of Two Numbers Is 4 Less Than Twice The Larger. If The Larger Is Decreased By Three Times The Smaller, The Result Is -20. Can You Find The Numbers.?

Let L represent the larger number, S represent the smaller number.
S + L = 2L - 4    (The sum of the two numbers is 4 less than twice the larger)
L - 3S = -20    (The larger decreased by 3 times the smaller gives -20)

Solve the first for S
S = L - 4    (subtract L from both sides of the first equation)

L - 3(L -4) = -20    (substitute the expression for S into the second equation)
L -3L +12 = -20    (use the distributive property to get rid of the parentheses)
-2L = -32    (subtract 12 from both sides of the equation)
L = 16    (divide the equation by -2)
S = 16 -4 = 12    (use the expression for S to determine S from L)

The numbers are 12 and 16.
thanked the writer.
Anonymous commented
If u plug it in to check. It not working
Oddman commented
Perhaps you're using different rules of arithmetic than I am.
The sum of the two numbers is 12+16=28. Twice the larger is 2*16=32. The sum is 4 less than twice the larger: 28=32-4.
Three times the smaller is 3*12=36. The larger decreased by that amount is 16-36=-20.
I'd be happy to have you demonstrate where I went wrong. 