Question

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.

Answer 1

The entire expression should be subtracted from 30. To subtract the quantity, distribute the negative sign, which changes the signs on the terms. So, the –2 changes to positive and gets added to 30 instead of subtracted from it

Answer 2

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

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.