Math: b8e73b5b

ID: b8e73b5b

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

Comment: Read the question carefully.

Method 1: Note that in this word problem, Ken has already worked 10 hours this week, and the question asks how many more hours he would need to work to reach his target savings of at least $270—i.e. the question is not asking how many total hours Ken will need to work for the week. It is given that he earned $8 per hour at first and $10 per hour thereafter. Also, he saves 90% of what he earns. (I guess he does not pay taxes upfront.)

10 hours * $8 per hour = $80

At this point, with a reasonable understanding of percents, we can eyeball the answers and pick a winner from the lineup. 10 percent of any number is that number with the decimal pushed one space to the left. Thus, if we know Ken's gross earnings, 80 + something, we can quickly subtract 10 percent and be close enough to deduce what must be correct. The answers here are pretty specific with the units digit, but we can work with easier values in between those given to tease out certain truths. For instance, note the divide between (B) and (C), 33 versus 22. We can easily test 30, which will allow us to rule out (A) and (B) or (C) and (D).

30 hours * $10 per hour = $300

$300 + $80 = $380

$380 - $38 = $342 (too high)

Because 342 > 270, it must not be true that Ken will need to work at least 30 more hours, let alone 33 or 38, so get rid of (A) and (B). The correct answer must be (C) or (D), and we can use 20 as a simple sounding board between them, since, again, there is no need to get too particular between 22 and 16.

20 hours * $10 per hour = $200

$200 + $80 = $280

$280 - $28 = $252 (not enough)

Clearly, Ken will need to work more than 20 more hours to reach his savings goal, so the correct answer must be (C), 22. When you let go of needless details, you can streamline your solving process. The above solution might take a minute, provided you are confident with percents.

Method 2: You can use Desmos to work out some of the arithmetic and generate an inequality. If it helps, think of the inequality in terms of words.

90 percent of $8 * 10 hours and $10 * so many hours must be at least $270

0.90(80 + 10x) ≥ 270

The graph shows the solution: Ken must work at least 22 hours more to save at least $270. The correct answer is (C).

Method 3: Using the same method as that outlined above, but without graphing the solution, you could work out the algebra yourself and maybe use the calculator for the arithmetic. I will use h for "hours," since it seems more intuitive to me, and good organization is never a bad idea.

0.90(80 + 10h) ≥ 270

72 + 9h ≥ 270

9h ≥ 198

h ≥ 22

The correct answer is (C).

Finally, you could lean on the answer choices, knowing that one of them must be the value that would lead to Ken saving $270 or more. The process works the same way, only backwards.