Number, Percent and Geometry 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 :

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

E  =  S + B - 5

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

lw  =  h + 10

3. The sum of two consecutive integers is 29.

n + (n + 1)  =  29

4. The product of two consecutive even integers is 168.

2n (2n + 2)  =  168

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? Below are some geometrical facts.

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

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

3. Sum of the angles of a triangle is 180.

4. The perimeter is the sum of the sides.

5. 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