Number Problems
Number problems are often set in a
context, typically involving money or an
amount of an item. To be confident at
solving number problems, it is essential to
understand the basics of fractions,
decimals, percentages and ratio.
Example 1
Ninety-six golf balls were picked
up at the driving range and
placed into two buckets. One
bucket has twenty-eight more
golf balls than the other bucket.
How many golf balls are in each
bucket?
Example 2
The sum of two consecutive
integers is sixty-five. Find the two
numbers.
Example 3
Five times a number increased by
seven is equal to forty-seven.
What is the number?
Example 4
The sum of three consecutive
odd integers is fifty-seven. Find
the three numbers.
Example 5
A college has two depositional
systems classes with a total of
two hundred thirty-seven
students. One class has forty-five
fewer students than the other
class. How many students are in
each class?
Digit word problems
are problems that involve
individual digits in integers and
how digits are related according
to the question. Some problems
would involve treating the digits
as individual numbers to be
related.
Example 1
The sum of the digits in a
two-digit number is eleven. If the
tens digit is three less than the
ones digit, find the number.
Example 2
In a three-digit number, the
hundreds digit is two more than
the tens digit. The ones digit is
two less than the tens digit. If the
sum of the digits is twenty-one,
find the number.
Example 3
The sum of the digits in a two-
digit number is nine. If the tens
digit is five more than the ones
digit, find the number.
Example 4
The sum of the digits in a two-
digit number is fourteen. If the
digits of the number are
reversed, the new number is
thirty-six more than the original
number. What is the original
number?
Example 5
The sum of the digits in a two-
digit number is thirteen. If the
digits of the number are
reversed, the new number is nine
more than the original number.
What is the original number?
Age problems
solving age problems, generally
the age of two different people
both now and in the future (or
past) are compared. The objective
of these problems is usually to
find each subject's current age.
Example 1
Paul is twenty-two years older
than his daughter Jessica. If
Jessica is forty-four years old,
how old is Paul?
Example 2
Jim is four years older than his
sister Kathy. If Jim and Kathy’s
ages add up to fifty-four, how old
are Jim and Kathy?
Example 3
Eleven years from now, Nicholas
will be three times as old as he
was twenty-five years ago. How
old is he now?
Example 4
Paul is eight years older his wife
Lisa. Twenty years ago, the sum
of their ages was twenty-four.
Find their present ages.
Example 5
Sam is twenty-six years older
than Brian. Eight years from now,
Sam will be three times as old as
Brian. Find their present age.
Distance problems
are word problems that
involve the distance an
object will travel at a
certain average rate for a
given period of time. The
formula for distance
problems is:
distance = rate × time or.
d = r × t.
Example 1
Two people ride their bikes from
the same place in opposite
directions. If they leave at the
same time and person A rides 1.5
times as fast as person B, and in 4
hours, they are 60 miles apart,
what are their riding speeds?
Example 2
Two people leave from two
towns that are 280 miles apart
and travel toward each other
along the same road. Person A
drives 16 miles/hour (mph)
slower than person B. If they
meet in 3.5 hours, at what speed
did each person travel?
Example 3
Suppose you leave your house by
bicycle and travel 10 miles per
hour. One hour later, your
brother leaves and travels down
the same road by car at 60 miles
per hour. How long, in hours to
the nearest tenth, does it take for
the car to overtake the bicycle?
Example 4
Suppose you ride a bicycle to a
store at a speed of 6 miles/hour.
You then walk home at a speed
of 2 miles/hour. The total round
trip time is 3hours. How far from
your starting point is the store?
Example 5
Two planes leave an airport and
fly in opposite directions. One
plane flies at 85 miles/hour and
the other plane flies at 75 miles
per hour. How many hours will it
take for the two planes to be 800
miles apart?
