Transcript Solving Word Problems for the Unknown

SOLVING FOR THE
UNKNOWN: A HOW-TO
APPROACH FOR SOLVING
EQUATIONS
McGraw-Hill/Irwin
Chapter Five
Copyright © 2014 by The McGraw-Hill Companies, Inc. All rights reserved.
LEARNING UNIT OBJECTIVES
LU 5-1: Solving Equations for the Unknown
1.
Explain the basic procedures used to solve equations for
the unknown.
List the five rules and the mechanical steps used to solve
for the unknown in seven situations; know how to check
the answers.
LU 5-2: Solving Word Problems for the Unknown
2.
1.
List the steps for solving word problems.
2.
Complete blueprint aids to solve word problems; check
the solutions.
5-2
TERMINOLOGY
Expression – A meaningful combination of numbers and letters
called terms.
Equation – A mathematical statement with an equal sign showing
that a mathematical expression on the left equals the
mathematical expression on the right.
Formula – An equation that expresses in symbols a general fact,
rule, or principle.
Variables and constants are terms of mathematical expressions.
5-3
SOLVING EQUATIONS FOR THE
UNKNOWN
Equality in equations
A+8
58
Left side of equation
Right side of equation
Dick’s age in 8 years will equal 58.
5-4
VARIABLES AND CONSTANTS RULES
1. If no number is in front of a letter, it is a 1:
B = 1B; C = 1C
2. If no sign is in front of a letter or number, it is a +:
C = +C; 4 = +4
5-5
SOLVING FOR THE UNKNOWN RULE
Whatever you do to one side of
an equation, you must do to the
other side.
5-6
OPPOSITE PROCESS RULE
If an equation indicates a
process such as addition,
subtraction, multiplication, or
division, solve for the unknown
or variable by using the opposite
process.
5-7
OPPOSITE PROCESS RULE
A + 8 = 58
-
A
8
- 8
= 50
8 is subtracted from
both sides of equation to
isolate variable A on the
left.
Check
50 + 8 = 58
5-8
EQUATION EQUALITY RULE
You can add the same quantity or number to
both sides of the equation and subtract the
same quantity or number from both sides of
the equation without affecting the equality of
the equation.
You can also divide or multiply both sides of
the equation by the same quantity or number
(except zero) without affecting the equality of
the equation.
5-9
EQUATION EQUALITY RULE
7G = 35
7G = 35
7
7
By dividing both sides
by 7, G equals 5.
G = 5
Check
7(5) = 35
5-10
MULTIPLE PROCESSES RULE
When solving for an unknown
that involves more than one
process, do the addition and
subtraction before the
multiplication and division.
5-11
MULTIPLE PROCESS RULE
H +2= 5
4
H +2= 5
4
-2
-2
4
H
4
=
H
4
= 4(3)
H
=
()
1. Move constant to right
side by subtracting 2
from both sides.
3
12
2. To isolate H, which is
divided by 4, we do the
opposite process and
multiply 4 times both
sides of the equation.
Check
12 + 2 = 5
4
3+2=5
5-12
PARENTHESES RULE
When equations contain parentheses (which
indicates grouping together), you solve for the
unknown by first multiplying each item inside the
parentheses by the number or letter just outside
the parentheses.
Then you continue to solve for the unknown with
the opposite process used in the equation. Do
the addition and subtraction first; then do the
multiplication and division.
5-13
PARENTHESES RULE
5(P - 4) = 20
5P – 20 = 20
+ 20 + 20
5P
= 40
5P
5
= 40
5
P
=
8
1. Parentheses tell us that everything
inside parentheses is multiplied by 5.
Multiply 5 by P and 5 by 4.
2. Add 20 to both sides to isolate 5P
on left.
3. To remove 5 in front of P, divide
both sides by 5 to result in P
equals 8.
Check
5(8 - 4) = 20
5(4)
= 20
20
= 20
5-14
LIKE UNKNOWN RULE
To solve equations with like
unknowns, you first combine the
unknowns and then solve with the
opposite process used in the
equation.
5-15
LIKE UNKNOWN RULE
4A + A = 20
5A
= 20
5A
5
= 20
5
A
To solve this equation:
4A + 1A = 5A. Thus, 5A
= 20. To solve for A,
divide both sides by 5,
leaving A equals 4.
=4
Check
4(4) +4 = 20
16 + 4 = 20
5-16
SOLVING WORD PROBLEMS FOR
UNKNOWNS
1) Read the entire problem.
3) Let a variable represent
the unknown.
Y = Computers
Read again if necessary!
2) Ask: “What is the problem
looking for?”
4) Visualize the relationship
between the unknowns and
variables. Then set up an
equation to solve for the
unknown(s).
4Y + Y = 600
5) Check your results to
ensure accuracy.
5-17
SOLVING WORD PROBLEMS FOR THE
UNKNOWN
Blueprint aid
Unknown(s)
Variable(s)
Relationship
5-18
SOLVING WORD PROBLEMS FOR THE
UNKNOWN
ICM Company sold 4 times as many computers as Ring Company. The
difference in their sales is 27. How many computers of each company were
sold?
Unknown(s)
Cars Sold:
ICM
Ring
Mechanical
Steps
4C -- C = 27
3C
= 27
3
3
C= 9
Variable(s)
4C
C
Relationship
4C
-- C
27
Ring = 9 computers
ICM = 4(9) = 36 computers
Check 36 - 9 = 27
5-19