Pre-Algebra Demystified

PRACTICE

1. A stick 56 inches long is broken into two pieces so that one piece is
   28 inches longer than the other piece. Find the length of each piece.


2. A person made two purchases. One purchase costs four times as much
   as the other purchase. The total cost of both purchases was $28. Find
   the cost of each purchase.


3. The difference between two numbers is 12. Find the values of each of
   the numbers if their sum is 28.


4. A mother is 4 times older than her daughter. In 14 years, she will be
   twice as old as her daughter. Find their ages now.


5. A house is worth four times as much as the lot it is built on. If the sum
   of the values of the house and lot is $156,000, find the value of each.

ANSWERS

1. 14 inches, 42 inches


2. $5.60, $22.40


3. 8, 20


4. mother’s age¼28; daughter’s age¼ 7


5. lot’s value¼$31,200; house’s value¼$124,800

Solving Percent Problems Using Equations

In Chapter 6 circles were used to solve percent problems. In Chapter 8
proportions will be used to solve percent problems. In this section, you
will see that percent problems can be solved using equations.
To solve a percent problem, write an equation using the numbers and the
word ‘‘of’’ as multiplication and the word ‘‘is’’ as an equal sign. The words
‘‘what number’’ or ‘‘what percent’’ translate to a variable such as x. Then solve
the equation for x.

EXAMPLE
42% of 500 is what number?

SOLUTION
Translate the statement into an equation:

what

42% of 500 is number?

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42 %  500 ¼ x

CHAPTER 7 Expression and Equations 147