Gabriel determined that his total cost would be represented by 2.5x + 2y – 2. his sister states that the expression should be x + x + 0.5x + y + y – 2. who is correct? explain.

  Both expressions are equivalent. There is not enough information here to let one say that one is "correct" and the other is not.

Step-by-step explanation:

Gabriel and his sister have arrived at expressions that give the same result when evaluated (except on some computers for some values of x and y*). We have no basis for deciding which of the two equivalent expressions is "correct."

The distributive property lets you "collect terms" by adding the coefficients of terms with the same variable:

  x + x + 0.5x = x(1 + 1 + 0.5) = 2.5x . . . . for example

When we collect terms in the sister's expression, we find it is identical to Gabriel's expression.

* About computer evaluation

The internal representation of numbers in binary computers is such that many numbers cannot be represented exactly. As a consequence, the order in which numbers get added can make a difference in the resulting value. In some cases, it may be preferable to compute x+x+0.5x, rather than 2.5x. This can depend, too, on the precise computer language used and the manner in which it is translated to the machine language actually executed by the computer.