


Tackling Storytime Algebra Items
There are two options for solving almost every Storytime
item:
 The Math Path—set up an algebraic equation, then solve.
 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

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 wronganswer 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 timeconsuming 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:

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.

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.

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.
