Math: daad7c32

ID: daad7c32 

(SAT Suite Question Bank > Find Questions > Assessment: SAT + Test: Math + Domain: Algebra)

Comment: It may help to reframe the equation in more familiar terms.

Method 1: Logically, an equation whose left-hand side refers to length must, in some way, have a right-hand side that also refers to length. What makes this a bit tricky is that we are told that w is a weight, in newtons, of an object hanging from a spring. Look at the equation:

l = 30 + 2w

length = length + [2 (of some unit) * newtons = length]

The 2 in question must be pulling double duty if a weight has to become a length. If it helps, you may want to consider the linear equation y = mx + b, in which m represents the slope, or rate of change, of the line. The equation above is just a dressed up version of the slope-intercept form of a line, and 2 must therefore represent the same sort of rate of change. Because answer choices (A) and (B) are not rates, they can safely be eliminated. Between (C) and (D), first off, the object should not change in weight just because it is suspended from a spring; second, remember the units of the equation, which measures length. If w increases by 1, that would affect the length the spring would stretch. The correct answer must be (D).

Method 2: You could model the equation using Desmos and, say, y for l and x for w.

Because the spring starts with a length of 30 centimeters, it can only increase when the weight is attached. Hover over the line and observe what happens as you slide up: (0, 30), (2, 34), (4, 38), and so on. In short, for each increase of 2 in x (standing in for w), the y-value (l) increases by 4 cm. This is just what answer choice (D) says, only with the numbers each divided by 2: the correct answer must be (D).

Method 3: You could substitute your own numbers into the equation to test what made sense. Since length, l, is dependent on w, you could manipulate w:

l = 30 + 2(1) --> 30 + 2 --> 32

l = 30 + 2(2) --> 30 + 4 --> 34

That is enough. It is clear that as w increases by 1, the length, l, increases by 2. Answer choice (C) reverses that relationship, making w dependent on l, and, as stated above, in method 1, (A) and (B) are not even rates of change, so they should not be in the running. The correct answer must be (D).