Story Problems

Once you know your basic operations (addition,
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:

For addition:

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

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:

Read the entire problem thoroughly
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.
Write out the number equation you’ll need to solve.
Complete the solving process carefully.
When you get your answer, reread the problem and ask yourself, “Does this answer
make sense?”
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.

Now, let’s try another one.

Now, let’s try a couple harder problems.

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.

Final answer: 408 ft².

{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.

Final answer: 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.

Final answer: $118.49

{$118.49}