Algebra
Tackling Storytime Algebra Items
There are two options for solving almost every Storytime item:
  1. The Math Path—set up an algebraic equation, then solve.
  2. The Backward Path—work backward from the answer choices to see which one is correct.
Both paths work. The Math Path, however, has more traps in it, because the distractors in the item are designed to trip someone up who takes the Math Path. It is, therefore, always safer to work backward from the answer choices. We emphasize the Backward Path because that’s the whole point of taking the SAT—to get as many right answers as possible on the test and to do it efficiently. The steps for the Backward Path are:
Step 1: Read through the item slowly.
Step 2: Pick an answer choice instead of a variable. If the item is filled with variables, assign the variables actual numbers so you’re working with real numbers, not abstract placeholders.
Step 3: Run the numbers through the necessary computations and see what you get.
Step 4: If the answer is incorrect, pick a different answer choice and try again.
Storytime Algebra in Slow Motion
7. At a popular sandwich shop, it takes 3 minutes for one sandwich maker to prepare a sandwich for a single customer. If lunchtime is from 11:30 a.m. to 1:00 p.m. and there are 390 customers, what is the MINIMUM number of sandwich makers needed to ensure that every customer gets served?
(A) 9
(B) 13
(C) 16
(D) 21
(E) 28
Step 1: Read through the item slowly.
The item is tempting you to set up an equation. You can do so if you feel confident, but you’re setting yourself up for a fall if you make a mistake. For now, just realize that the answer choices represent different numbers of sandwich makers.
Step 2: Pick an answer choice instead of a variable. If the item is filled with variables, assign the variables actual numbers.
Often, it’s a good idea to start with the middle answer, C. That way, if you run the computations and come up with an answer that’s too large, you can eliminate not just C but any answer choices larger than C as well. For our example, if C were too large, then D and E would be too large as well.
However, this item asks for the minimum number of sandwich makers that could do the job. With that in mind, it might be a better idea to start with choice A, the smallest number. If A doesn’t work, you can move up to choice B, and so on. Working the other way makes no sense, because even if you find a large number that works, you still have to check the smaller numbers to make sure they don’t work.
Step 3: Run the numbers and see what you get.
Let’s try answer choice A, which is 9 sandwich makers. Nine employees would make 9 sandwiches every 3 minutes. Lunchtime is 90 minutes total (11:30 a.m. to 1:00 p.m.). So:
(9 sandwiches/every 3 minutes)(90 minutes) = 270 sandwiches
Does this answer work? Well, no, it doesn’t. There are 390 customers, and only 270 would get served if there were 9 sandwich makers. So 9 is too small a number, and you know the answer has to be B, C, D, or E. If you were pressed for time, you could even take a guess right now and beat the wrong-answer penalty.
Step 4: If the answer is incorrect, try again.
Let’s try choice B. Thirteen workers could make 13 sandwiches every 3 minutes. So:
(13 sandwiches/every 3 minutes)(90 minutes) = 390 sandwiches
The math works, so that’s your answer. Pick B and move on.
This process is a bit more time-consuming than you might like it to be, but it’s a surefire way to get the item right. If you take the Math Path and make a tiny mistake, you’ll end up with one of the distractors and latch onto it.
Guided Practice
Here’s a Storytime Algebra item with variables in the stem and the answer choices:
10. Roald has j liters of orange juice that he plans to serve at a brunch. Two-thirds of the juice will go to the adults, who drink r liters each. The rest will go to the kids, each of whom will drink k liters apiece. Which of the following expressions gives the number of children that Roald will be able to supply with his orange juice?
(A)
(B)
(C)
(D)
(E)
Step 1: Read through the stem slowly.
The goal is to find the number of children that can be served. That may mean the number of adults is not crucial.
Step 2: Pick an answer choice instead of a variable. If the item is filled with variables, assign the variables actual numbers.
You have three variables: j, r, and k. Try to keep the numbers small, and make sure that j is a number that can be divided by many different numbers. Also, on this item you may want to avoid the number 1 because anything multiplied or divided by 1 remains 1.
Step 3: Run the numbers and see what you get.
After assigning numbers to all the variables, go through the answer choices and change every one of the choices from an algebra expression to an actual number by substituting your real numbers. Now take those same numbers and run them through the computations required in the item. This should give you a definite number that you will find in the answer choices.
Step 4: If the answer is incorrect, try again.
If you find two choices that both work, pick a different set of numbers and run it through again. If you’re pressed for time, you can always eliminate what you can and take a guess.
Guided Practice: Explanation
Step 1: Read through the stem slowly.
Reading the stem, the general trend is that you start with a total amount, subtract the amount that the adults are going to take, then take what’s remaining and divide it by the amount each child drinks. That will give you the total number of kids that Roald can serve.
Step 2: Pick an answer choice instead of a variable. If the item is filled with variables, assign the variables actual numbers.
Try this set of numbers:
j = 30
r = 3
k = 2
It doesn’t matter that 2 liters per child is a huge stomach load. What’s important is that you have a small number, 2, that differs from the adult number. Also, both 2 and 3 divide into 30, which should make the math much simpler.
Step 3: Run the numbers and see what you get.
Let’s convert every answer choice first.
(A)
(B)
(C)
(D)
(E)
Now run through the item using our real numbers. If Roald has j liters, then he has 30 liters of orange juice. The adults are going to drink 2/3 of it, so the amount they are drinking is: . If the adults drink 20 liters, then there’s only 30 – 20 = 10 liters left. If each kid drinks 2 (that’s k) liters, then 10 divided by 2 equals 5. That’s answer choice E.
Step 4: If the answer is incorrect, try again.
You can look at choice D, 60, which is way more than the correct answer of 5. D is there because it works as a good trap for a student trying to solve this item using the Math Path. By inserting real numbers, you avoid this trap.
Independent Practice
After you complete the following item, look on the following page for the explanation.
3. Eva has just inherited money from her uncle. After taxes, she received a net sum of $32,000. If the tax rate was 20%, how much was Eva’s total inheritance in dollars?
(A) 6,400
(B) 25,600
(C) 38,000
(D) 40,000
(E) 45,000
Independent Practice: Explanation
Step 1: Read through the stem slowly.
The dollar amount in the stem is what Eva received after paying taxes. That means the answer choices all show what the inheritance was before taxes.
Step 2: Pick an answer choice instead of a variable. If the item is filled with variables, assign the variables actual numbers.
If Eva received $32,000 after taxes, the amount must have been greater than $32,000 before taxes were paid. That means you can get rid of choices A and B right off the bat. The answer has to be C, D, or E. You should try D because it’s the middle number of the remaining answer choices. If D turns out to be too low, the answer has to be E because it is the only number greater. If 40,000 is too large, the answer must be C.
Step 3: Run the numbers and see what you get.
What is 20% of 40,000 (answer choice D)? (0.20)(40,000) = 8,000. Because the taxes on $40,000 are $8,000, Eva would receive $40,000 – $8,000 = $32,000. There’s your answer.
Step 4: If the answer is incorrect, try again.
Using our heads to eliminate A and B, and running D first allowed us to skip this step, no matter what the outcome was.
Help | Feedback | Make a request | Report an error