Number, Percent and Geometry Problems

I.  Midterm I

II.  Number Problems

Some 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

Exercises: Convert to a math expression :

 Elizabeth is five years younger than the combined age of Sarah and Brian.

The product of the length and the width is 10 more than the height.

The sum of two consecutive integers is 29.

The product of two consecutive even integers is 168.

III.  Percent Problems

The words percent of mean /100 x

for example 20 percent of 50 means (20/100)(50)

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 + .15x = 11.50 or 1.15x = 11.50 or x = 11.50/1.15 = $10.   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?

IV.  Geometry Problems

Known facts:  

1)  Area of a triangle = 1/2 bh

2)  Area of a rectangle = bh

3)  sum of the angles of a triangle is 180.

4)  the perimeter is the sum of the sides

5)  iscoceles 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 or

3x + 30 =180

3x = 150

x = 150/3

x = 50