Transcript Chapter 4.1 Objective One

Chapter 4.1 Objective One
Translate a Sentence
into an Equation & Solve
Recall, equation is the mathematical statement
that two expressions are equal to one another.
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First Step, Identify where the equal sign is to
be placed.
Second Step, Translate the verbal statements
into variable expressions.
Third Step, Simplify expressions and solve for
the unknown value.
Fourth Step, Check your answer!
Translate “nine less than a twice number is five times the sum of
the number and twelve” into and equation and solve.
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First Step, Identify where the equal sign is to be placed.
“nine less than twice a number = five times the sum of the
number and twelve”
Second Step, Translate the verbal expressions to variable
expressions. Let n represent the number.
2n – 9 = 5 (n + 12)
Simplify expression. 2n – 9 = 5n + 60
Solve for unknown.
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2n – 9 = 5n + 60
- 2n -60 = - 2n - 60
-69 = 3n
- 23 = n
Fourth Step check your answer by substitution.
2n – 9 = 5 (n + 12)
2(-23) – 9 = 5 ((-23) + 12)
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-46 - 9 = 5(-11)
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- 55 = -55
Checks!
Five more than four times a number is thirteen. Find
the number.
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First Step, Identify where the equal sign is to
be placed.
Five more than four times a number = thirteen.
Second Step, Translate the verbal expressions
to variable expressions. Let n represent the
number.
4n + 5 = 13
Solve for unknown.
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4n + 5 = 13
-5= -5
4n = 8
n=2
Fourth Step check your answer by substitution.
4(2) + 5 = 13
8 + 5 = 13
13 = 13 Check!
The sum of seven times a number and three is
the opposite of eighteen. Find the number.
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1st The sum of seven times a number and three = the
opposite of eighteen.
2nd
7n + 3 = -18
3rd
7n + 3 = -18
-3
- 3
7n = -21
n=-3
4th
7(- 3) + 3 = -18
-21+3 = -18
-18 = -18 Checks !
NOW YOU TRY!
Write an equations and solve the following.
The difference between six times a number and four
times a number is negative fourteen.
Answer: 6n - 4n = -14;
n = -7
2. Four times a number is three times the difference
between thirty-five and the number.
Answer: 4n = 3(35 - n);
n = 15
3.
The sum of two numbers is two. The difference
between eight and twice the smaller number is two
less than four times the larger. Let n be the smaller
number and (2-n) the larger number.
Answer: 8 – 2n = 4 (2 - n) - 2;
-1 and 3
1.
Chapter 4.1 Objective Two
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Application Problems
Answers to application problems must have
units, e.g. feet, degree, dollars, …
When defining a problem, relate the term(s) to
one variable.
A molecule of octane gas has eight carbon atoms. This represents
twice the carbon atoms in a butane gas molecule. Find the
number of carbon atoms in a butane molecule.
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Let n represent the unknown.
Octane Gas has eight Carbon Atoms, and
Butane twice the atoms.
8 = 2n
Solving for n
n = 4
There are four Carbon Atoms in a molecule of
Butane Gas.
A board ten feet long is cut into two pieces. Three times the
length of the shorter piece is twice the length of the longer piece.
Find the length of each piece.
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Let n be the length of the longer piece and
(10 – n) be the shorter piece.
Translate verbal into variable expressions.
3(10-n) = 2n Solve for n
30 -3n = 2n
30 = 5n
n = 6 ft. Longer piece
10 – 6 = 4 ft. Shorter Piece
NOW YOU TRY!
Write an equation and solve the following.
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1. Greek architects considered a rectangle whose length was
approximately 1.6 times its width to be most visually appealing.
If the width and length a given rectangle equals 130 feet, what
are the length and width?
Answer: w+1.6w = 130;
w = 50ft , l = 80ft
2. A 20-foot board is cut into two pieces. Twice the length of
the shorter piece is 4-feet more than the length of the longer
piece. Find the length of the shorter piece. Hint let x = shorter
piece.
Answer: 2x = ( 20 - x ) + 4;
Shorter piece = 8 ft.
3. A technical information hotline charges $9.00 plus $050 per
minute to answer questions about software. If the costumer is
charged $14.50, how many minutes did the call take?
Answer: $9.00 + .5(min.) = $14.50;
11 Minutes