1. Translate a Sentence into an Equation & Solve
Chapter 4.1 Objective One
Translate a Sentence
into an Equation & Solve

2. Recall, equation is the mathematical statement that two expressions are equal to one another.
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!

3. Translate “nine less than a twice number is five times the sum of the number and twelve” into and equation and solve.
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

4. Solve for unknown. -46 - 9 = 5(-11) 2n – 9 = 5n + 60
Fourth Step check your answer by substitution.
2n – 9 = 5 (n + 12)
2(-23) – 9 = 5 ((-23) + 12)
= 5(-11)
- 55 = Checks!

5. Five more than four times a number is thirteen. Find the number.
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 n + 5 = 13

6. Solve for unknown. 4n + 5 = 13 - 5 = - 5 4n = 8 n = 2
- 5 = - 5
4n = 8
n = 2
Fourth Step check your answer by substitution.
4(2) + 5 = 13
8 + 5 = 13
13 = Check!

7. The sum of seven times a number and three is the opposite of eighteen
The sum of seven times a number and three is the opposite of eighteen. Find the number.
1st The sum of seven times a number and three = the opposite of eighteen.
2nd n + 3 = -18
3rd n + 3 = -18
7n = -21
n = - 3
4th (- 3) + 3 = -18
-21+3 = -18
-18 = Checks !

8. 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
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; and 3

9. Chapter 4.1 Objective Two 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.

10. Let n represent the unknown.
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.
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.

11. Translate verbal into variable expressions. 3(10-n) = 2n Solve for n
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.
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

12. NOW YOU TRY! Write an equation and solve the following.
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: $ (min.) = $14.50; Minutes