Let the function a@b be defined as 3a + 2b for all real numbers a and b. If u and v are real numbers for which u@v =v@u = 20, what is the value of 2u@3v?

Answer 1

a@b = 3a + 2b

u@v = 3u + 2v = 20
v@u = 3v + 2u = 20
add them: 5u + 5v = 40
u + v = 8

then 2u@3v
= 6u + 6v
= 6(u+v) = 6(20) = 120

Answer 2

a@b=3a+2b

u@v=v@u=20 u=v
If u and v both = 4 then 3(4)+2(4)=12+8=20
u=4 v=4
2u@3v=2(4)@3(4)=6(4)+6(4)=24+24=48