Math: 2937ef4f

 ID: 2937ef4f

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

Comment: Generally, word problems only need to be read for the numbers they provide that relate to the question being asked. In this question, for instance, we do not care that Hector is using an auger, nor, for that matter, that the rate of the machine is constant, because the passage later provides the conditional statement, If the auger continues to remove corn at this rate. With the numbers provided, that is all we need to work out the total number of hours the job will take.

Method 1: Forget about the exact values. Estimate. The difference between 24,000 and 19,350 is about 5,000 (rounded to the nearest thousand), and that took 5 hours. To get to roughly 13,000 (12,840 hardly matters), it stands to reason that since 19,350 and 13,000 are about 6,000 apart, at the same rate, the job will take another 6 hours or so. Alternatively, 24,000 and 13,000 are 11,000 apart, so the job should take about 11 hours, give or take. Looking at the answer choices, only (D) is greater than 10, so the answer must be (D). Nothing else makes sense.

Method 2: You could model the linear relationship using the points (0, 24,000) and (5, 19,350) if you really wanted to go by the book, but there is nothing wrong with using smaller values to keep the y-axis more manageable—say, (0, 24) and (5, 19.35). Pushing the decimal to the left 3 places can save time. To input the line, work out some of the basic algebra.

y = mx + b

y = [(24 - 19.35)/(0 - 5)]x + b

y = -(4.65/5)x + (24)

Of course, you know the y-intercept from the point (0, 24). All you need to do is graph and look for when y = 12.84, our decimal equivalent of 12,840. You can even go to Edit List (the gear icon) and Create Table to simply input the answer choices as the four x-values to track.

The answer is in plain sight from the table that automatically calculates the corresponding y-value for each input. Once again, the answer is (D).

Method 3: It is fine to work out the exact numbers in a more textbook fashion, even if the extra work is unnecessary. I will write an arithmetic solution below, but you could also use algebra. With a calculator at your disposal, the numbers should not prove daunting. All you have to do is make sure your information is organized—i.e. you know what the numbers mean.

24,000 - 19,350 = 4,650 (bushels removed) in 5 hours

4,650/5 = 930 bushels per hour

24,000 - 12,840 = 11,160 (bushels removed)

11,160/930 = 12

The answer is (D).