Math: ee2f611f

ID: ee2f611f

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

Comment: Be careful when dealing with real-world contexts and rounding.

Method 1: Read the question and consider the logical implications of the minimum number of trips. To minimize these trips, we would want to maximize the cost: simply put, someone could take fewer trips for $3.50 per trip than for $1.50. (For, say, $10.50, someone could take 3 trips at $3.50 apiece or 7 trips at $1.50 apiece.) Anything in between these extremes in cost is a distraction, so ignore the $2.50 tickets. Now, work with that calculator:

$95/$3.50 (per trip) ~ 27.14 trips

But how can someone take 14/100 of a trip? Just as someone cannot purchase a partial ticket, neither can someone take a partial trip, and if 27.14 represents the mathematical minimum number of trips someone could take, then we cannot round down to 27. Why? Not that I would recommend doing this during a live exam (unless you had a lot of time to spare), but you could compare the cost of purchasing individual tickets or that of the pass to see that 27 trips would be cheaper to pay for individually.

$3.50/trip * 27 trips = $94.50

Cost of pass = $95.00

$94.50 < $95.00

The same cannot be said if we round 27.14 up to 28 trips. Building off of the same work, we can see that the pass would be cheaper.

$94.50 (cost of 27 trips) + $3.50 (cost of 1 additional trip) = $98.00

$98.00 > $95.00

Thus, the correct answer must be 28.

I cannot emphasize this enough—when you encounter a word problem and derive a non-integer answer, consider the context. Sometimes you may have to round up when you are accustomed to rounding down, as we see here, and other times, you may have to round down when you would typically round up. For instance, if you saw a problem that imposed a weight limit on a cargo that consisted of identical boxes with identical parts inside, and you calculated something like 1249.99 (boxes), you would still have to round down to 1249 to ensure that the cargo did not weigh too much. Watch out for those assumptions.

Method 2: This question is no match for Desmos. All you have to do is create four linear graphs and check to see which one answers the question.

The purple line meets the red line at the lowest value for x, and once again, you have to think about how to interpret the excess after the decimal. For reasons stated above, the correct answer must be 28, not 27, and certainly not 27.14.

Method 3: It is fine to solve the problem algebraically rather than arithmetically, but it is not necessary to do so, and in my experience, more students waste more time trying to think of how to set up a problem the way they would in math class than if they just jumped in and used the numbers provided.