Answer math question = TEN points! (correct though)?

1. On Saturn, the inhabitants use the same mathematical operators that we do (+,-,etc), and they also use an operator @ that we do not know. Scientist have also determined that the following is true for any real numbers x and y:


x@0 = x


x@y = y@x


(x + 1)@y = (x@y) + y + 1


1. What is the value of 12@5?


a. 53 b.59 c.65 d.71 e.77





2. On a school trip to Saturn you must solve the equation 5@x = 17 in order to return to Earth. Under the same conditions as in the statement in question 1 above what is the value of x?


a.1 b.2 c.3 d.4 e.5

Answer math question = TEN points! (correct though)?
1


1@5 = 0@5 + 5 + 1 = 5@0 + 6 = 5 + 6 = 11


2@5 = 1@5 + 6 = 11 + 6 = 17


3@5 = 2@5 + 6 = 17 + 6 = 23


so n@5 = 5 + 6n, and 12@5 = 5 + 72 = 77





2


1@x = 0@x + x + 1 = x@0 + x + 1 = 2x + 1


2@x = 1@x + x + 1 = (2x + 1) + x + 1 = 3x + 2


looks like n@x = (n+1)x + n


so 5@x = 6x + 5 = 17, 6x = 12, x = 2