The document defines two operations, + and *, and their properties for real numbers a and b. It then uses these operations to solve the equation 4 + 15y = 5y + 16. The solution shows that y = 1.2.

1. April 6, 2009
Let the operations and be
defined for all real numbers a and b as
follows:
a b = a + 3b
a b = a + 4b
If 4 (5y) = (5y) 4, what is the
value of y?
4 + 15y = 5y + 16
­5y ­5y
4 + 10y = 16
­4
­4
10y = 12
y = 1.2

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