Number, Percent and Geometry Problems
Number Problems
To solve a word problem, it is helpful to remember some basic vocabulary:
Symbol 
Terms 
Examples 
+ 
sum
more than 
The sum of two numbers is
five more than one number 
 
difference
less than 
the length and the width differ by
three dollars less than the cost of a ticket 
x 
product 
the product of two numbers 
/ 
quotient 
the quotient of two numbers 
= 
is 
the length is twice the width 
Examples
Convert to a math expression :

Elizabeth is five years younger than the combined age of Sarah and
Brian.
E = S + B  5

The product of the length and the width is 10 more than the height.
lw = h + 10

The sum of two consecutive integers is 29.
n + (n + 1) = 29

The product of two consecutive even integers is 168.
2n (2n + 2) = 168
Percent Problems
The words "percent of" mean
"/100"
Example
20 percent of 50 means
20
50
100
Example
The price of a meal and a 15% tip was $11.50. What was
the price of the meal?
Solution
Let x be the price of the meal.
Then
x + 0.15x
= 11.50
Price of meal
+ 15/100 times the price of the meal
or
1.15x
= 11.50
Combining like terms
or
11.50
x =
= $10
1.15
Hence the price of the meal
was $10.
Exercise:
$800 is invested into an account paying 3% interest.
How much money should be invested into an account paying 4% interest
so that the total interest earned is $30?
Geometry Problems
Below are some geometrical facts.

Area of a triangle = 1/2 bh
(b is the base and h
is the height)

Area of a rectangle = bh (b is the base and h
is
the height)

Sum of the angles of a triangle is 180.

The perimeter is the sum of the sides.

Isosceles means two sides (and two angles) are equal.
Example
Find the angles of a triangle if the smallest angle
is 5 degrees less than the next smallest, which is
20 degrees less than the
largest.
Solution:
Let x be the measure of the smallest angle. Then
the middle angle has measure
5 + x
and the largest has measure
20 + (5 + x)
We have:
x + (5 + x) + (25+ x)
= 180 Sum of the angles of a triangle is
180
3x + 30
= 180
x + x + x = 3x, 5 + 25 = 30
3x = 150
Subtracting
30 on both sides
x =
150/3
Dividing by three
x = 50
Back to Math
152A Home Page
Back to the Math Department
Home
email
Questions and Suggestions
