# Story Problems

subtraction,
multiplication,
division),
you will encounter story problems, also known as word problems, which require you
to read a problem and decide which operation to perform in order to get the answer.
There are key words here that often indicate which operation you will use. We will
give you a list of them, but remember that for many problems, there may not be a
key word, and you’ll have to use your best judgment in order to figure out what
to do!

Here are the key words:

In addition to, sum, total, more than, altogether, in all, combined, extra, raise,

For subtraction:

How many more, difference, how many less, fewer, left (sometimes, left over), change,
lost, decreased (by), less, remain, take away

For multiplication:

How many times, times, multiplied by, of, every, product, by, twice as much, three
times as much (and so on), rate, at this rate, doubled, tripled (and so on), in
all

For division:

How much/many will each receive?, divided among, split up between, per, ratio, percent,
each, divide (or split) evenly, cut, average, share, quotient, equally (split, divided,
etc)

For telling that something equals another amount:

is/are, yields

In order to solve a story (word) problem successfully:

1. Read the entire problem thoroughly
2. Make a list of the numerical (number) information you’ll need. If the numbers have
units attached (for example, 12 inches), make sure you attach units in your list
so you don’t get confused.
3. Write out the number equation you’ll need to solve.
4. Complete the solving process carefully.
make sense?”
6. Remember to label your answer with the correct units, if needed.

## Example Story Problems

In this section, we’ll give you several examples of story (word) problems, starting
with simple problems and working up towards more complex problems.

Nick had 8 toy trucks in his toy box. His friend Nathan brought over 3 more toy
trucks. How many toy trucks did the boys have altogether?

What is the key word in this problem?

If you look back at the list of key words at the top of the page, you’ll find that
altogether listed as a key word.

altogether

Altogether is our key word. Now, what operation will we have to perform to get the

A.
B.
Subtraction
C.
Multiplication
D.
Division

The correct answer here would be A.

We know we’ll have to do addition, because altogether is a key word that means adding.

Now, what will our problem look like?

A.
9 + 1
B.
3 + 6
C.
8 + 3
D.
7 + 2

The correct answer here would be C.

We know we’ll be adding together 8 + 3, because those were the two numbers mentioned
in the problem.

What is 8 + 3?

A.
13
B.
10
C.
8
D.
11

The correct answer here would be D.

Therefore, our answer is 11 toy trucks altogether.

Now, let’s try another one.

John had 15 books on his bookshelf. John’s dog, Buster, came in and slobbered all
over four of them. How many books did John have left that were not slobbered on?

What is the key word in this problem?

If you look back at the list of key words at the top of the page, you’ll find that
left is listed as a key word.

left

Left is our key word. Now, what operation will we have to perform to get the answer
to this problem?

A.
B.
Subtraction
C.
Multiplication
D.
Division

The correct answer here would be B.

We know we’ll have to do subtraction, because left is a key word that means subtract.

This problem is a subtraction problem. Now, let’s get it set up. How will this problem
look?

A.
15 + 4
B.
4 – 15
C.
4 + 15
D.
15 – 4

The correct answer here would be D.

We know we’ll be subtracting 15 – 4, because those were the two numbers mentioned
in the problem.

Now, perform the subtraction. What is 15 – 4?

A.
13
B.
12
C.
11
D.
10

The correct answer here would be C.

Our final answer is 11 books.

Now, let’s try a couple harder problems.

Dan is getting ready to go to a concert. He wants to figure out how many people
will be there. He knows that there are 250 rows of seats, and each row has 40 seats
in it. How many seats are there in the concert hall in all?

What is the key word in this problem?

If you look back at the list of key words at the top of the page, you’ll find that
in all is listed as a key word.

in all

In all is our key word. Now, what operation will we have to perform to get the answer
to this problem?

A.
B.
Subtraction
C.
Multiplication
D.
Division

The correct answer here would be C.

We choose multiplication because we see the keyword in all, but also because it
makes sense. Essentially this may be seen as an addition problem, which is why the
keyword is also in the addition section, but since the adding of the rows would
all be the same, we can multiply to make the process faster.

This problem is a multiplication problem. Now, let’s get it set up. How will this
problem look?

A.
250 x 40
B.
250 / 40
C.
250 – 40
D.
240 x 5

The correct answer here would be A.

We would use 250 x 40 because we decided that this is a multiplication problem.
Since we want to figure out a total number of seats in the hall, we’re going to
multiply the two given numbers together, as if we were calculating area.

Now, perform the multiplication. What is 250 x 40?

A.
11,500
B.
12,000
C.
10,000
D.
10,500

The correct answer here would be C.

Our final answer is that there are 10,000 seats at the concert Dan is attending.

Let’s look at one more example. Three friends go out to dinner. Near the end, they
get the bill and they owe the restaurant \$27.89. They want to split the bill evenly
between the three of them. How much will each person pay?

What is the key word in this problem?

If you look back at the list of key words at the top of the page, you’ll find that
split evenly is listed as a key word.

{split|split the bill evenly|evenly|even}

Evenly is our key word. Now, what operation will we have to perform to get the answer
to this problem?

A.
B.
Subtraction
C.
Multiplication
D.
Division

The correct answer here would be D.

We choose division because we see the keywords “split” and “evenly.” Also, division
makes sense because they want to divide the bill between three people. Because they’re
splitting it up, we would choose division.

This problem is a division problem. Now, let’s get it set up. What would our equation
be?

A.
\$27.89 / 3
B.
3 / \$27.89
C.
3 x \$27.89
D.
\$27.89 x 3

The correct answer here would be A.

We choose \$27.89 / 3 because we know we have to split up the amount of money, \$27.89,
between the three friends, so we know we have to divide by three.

Now, perform the division. What is \$27.89 / 3? (Round to the nearest cent)

A.
\$9.25
B.
\$10.30
C.
\$9.30
D.
\$10.29

The correct answer here would be C.

When we divide, we get an answer of 9.2966666, with a repeating 6 at the end. We
want to round it to the nearest cent, which is the hundredths place after the decimal.
We see that that number is already a 9, and a 6 after it means round up. However,
we can’t make one place value a ten, so we increase the tenths digit by one, turning
the 2 into a 3. If this doesn’t make sense, please read
rounding numbers

Now, let’s go through some harder story (word) problems. All of the story problems
we’ve done have had only one step, and we’ve been able to easily decide if they
are addition, subtraction, multiplication, or division. However, some story problems
have more than one step, involving more than one key word and/or operation. We’ll
show you a few of these now.

Carly is making a dress. She needs 1 yard of yellow fabric, 1.5 yards of purple
fabric, and .5 yards of green fabric. Yellow fabric costs \$5.95 per yard, purple
fabric costs \$3.95 per yard, and green fabric is on sale for \$7.00 per yard. How
much will she spend in all if she buys just enough fabric to make her dress? (Ignore
tax in your calculations). Click Next Step for the first part of the solution.

First, we have to figure out how much Carly is spending on each amount of fabric;
then, we can use the key word “in all” which tells us that we need to add the amounts
together for a final total. In order to figure out how much each piece of fabric
costs, we need to multiply the price by the amount she needs to get a total.

First, let’s calculate the yellow fabric cost. She needs one yard, and it costs
\$5.95 per yard, so she’ll be spending \$5.95.

Now, let’s calculate the purple fabric cost. She needs 1.5 yards, and it costs \$3.95
per yard; therefore we have to multiply 1.5 times \$3.95, which comes out to be \$5.93
(we round to the nearest cent).

Finally, let’s calculate the green fabric cost. The green fabric is on sale for
\$7.00 per yard, and she needs .5 yards of it, so we multiply \$7.00 times .5 and
get \$3.50.

Now, we have three money amounts (one for each color fabric) that we can now add
together to get a total amount that Carly will spend. We know that we have to add
these amounts together, like this:

\$5.95 + \$5.93 + \$3.50 = \$15.38

Thus, our final answer is that Carly will spend \$15.38 on fabric for her dress.

Now, we’ll give you one to practice on. John is planning to carpet three rooms in
his house. One room is 15 by 12 feet, one room is 17 by 14 feet, and the last room
is 10 by 12 feet. John has 130 square feet of carpeting already. How much more carpeting
does he need in order to carpet all three rooms?

First, you have to figure out how many square feet he has to carpet overall. That
means we need to figure out the area of each room, and add those together. We multiply
the dimensions together as follows:
15 x 12 = 180 ft2
17 x 14 = 238 ft2

10 x 12 = 120 ft2

Now, we have the area of each floor he has to carpet, so we can add these all together
to find out the total amount of carpeting he needs.

180 + 238 + 120 = 538 ft2. This is the total amount John will need. However,
the problem said that he already has 130 ft2 of carpet, so we need to
figure out how much more he needs. Therefore, we need to subtract 130 from 538,
and we get 408 ft2 leftover. This is how much more carpeting John will
need to finish off his three rooms.

{408 square feet|408|408 sq ft|408 ft2}

The Smith family is going to take a vacation to Florida. They live in Illinois,
and have figured out that the trip is 1,150 miles from their house to the hotel
in Florida. They get 28 miles per gallon of gas, and plan on travelling at an average
rate of 60 miles per hour. Gas costs about \$2.89 per gallon.

a) How long will it take them to get to Florida? (in hours)

For this part, you divide the total miles (1,150) by the speed they’re travelling
(60 mph) and you would get 19.16666 (repeating). You would round the answer to 19.2
hours.

{19.2 hours|19.2 hrs|19.2 h}

b) How much money should they leave for gasoline (going one way)?

First, you would divide the total number of miles (1,150) by the amount of miles
they get per gallon of gas (28); this gives you 41 gallons—the total amount needed
for the trip. Then, you would multiply the number of gallons (41) by the cost per
gallon of gas (\$2.89) and round to the nearest cent, which gives you \$118.49. This
is the amount they should save for gas going one way.