Solved Examples and Worksheet for Translate Between Algebraic Expressions and Verbal Phrases.

Q1A rope is cut into 7 equal pieces. A small piece of 2 ft is again cut from each of the 7 pieces. Choose the correct variable expression for the new length of each piece.

A. (x7 - 2) ft
B. (x2 - 7) ft
C. (2 - x7) ft
D. (x7 + 2) ft

Solutions
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Step: 1
Let x be the length of the original rope.
Step: 2
Length of each of the 7 pieces = x7 ft
Step: 3
The variable expression for the new length of each piece is (x7- 2) ft.
  [A length of 2 ft is cut from each of the 7 pieces.]
Correct Answer is :   (x7 - 2) ft
Q2Identify a variable expression for the word phrase '13 more than 8 times a number'.
A. 13n + 8
B. 8n + 13
C. n + 91
D. 8n - 13

Solutions
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Step: 1
Let n be a number.
Step: 2
13 more than 8 times a number = 8n + 13.
  [Write the expression.]
Step: 3
So, the variable expression for the phrase is 8n + 13.
Correct Answer is :   8n + 13
Q3Choose a variable expression for the phrase, '15 less than 6 times a number'.
A. 6n + 15
B. 6 + n - 15
C. 6 +15n
D. 6n - 15

Solutions
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Step: 1
Let an unknown number be "n".
Step: 2
6 times the number = 6 × n = 6n.
  [Multiply.]
Step: 3
15 less than 6 times the number = 6n - 15.
  [Subtract.]
Correct Answer is :   6n - 15
Q4Kim's age is 4 years less than twice the age of her brother. Choose a variable expression for this situation.
A. 2 + n + 4
B. 2n - 4
C. n - 4
D. 2n + 4

Solutions
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Step: 1
Let n represent the age of Kim's brother.
Step: 2
Twice the age of Kim's brother is 2n.
Step: 3
4 years less than twice the age of Kim's brother is 2n - 4.
Correct Answer is :   2n - 4
Q5Lindsay's salary was $y 3 years ago. Now, she gets 4 times her previous salary and she spends $1512. Calculate her savings.

A. $(1512 + 4y)
B. $(1512 - y)
C. $(1512 - 4y)
D. $(4y - 1512)

Solutions
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Step: 1
Lindsay's present salary is $4y.
Step: 2
Lindsay's savings = $(4y - 1512)
  [Savings = Income - Expenditure.]
Correct Answer is :   $(4y - 1512)
Q6Paul and Matt fire 46 shots each to hit a target. Each person gets p points for a hit and loses q points for a miss. Paul hits the mark 40 times and Matt hits the mark 38 times. Identify the variable expressions for their individual scores.

A. 40p - 6, 38p - 8
B. 40p, 38q
C. 40p - 6q, 38p - 8q
D. 38p, 40q

Solutions
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Step: 1
Points scored by each person = Number of hits × p - Number of missed hits × q
Step: 2
Number of hits that Paul missed = (46 - 40) = 6
  [Subtract.]
Step: 3
The variable expression for the points scored by Paul is 40p - 6q.
Step: 4
Number of hits that Matt missed = (46 - 38) = 8
  [Subtract.]
Step: 5
The variable expression for the points scored by Matt is 38p - 8q.
Step: 6
So, the variable expressions for the points scored by Paul and Matt are 40p - 6q and 38p - 8q.
Correct Answer is :   40p - 6q, 38p - 8q
Q7Which of the following is the correct choice for the statement, "y is divided by a number 38"?

A. y - 38
B. y + 38
C. y38
D. 38y

Solutions
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Step: 1
y is divided by a number 38.
  [In words.]
Step: 2
y38
  [Variable expression.]
Step: 3
Variable expression for the word phrase is y38.
Correct Answer is :   y38
Q8Which of the choices represents the word phrase "4 less than half of m" ?
A. 4 - m2
B. 2m - 4
C. m2 - 4
D. m - 42

Solutions
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Step: 1
Half of m = m2
Step: 2
4 less than half of m = m2 - 4.
Correct Answer is :   m2 - 4
Q9Choose a variable expression for the phrase, '13 more than 8 times a number'.

A. 8n + 13
B. 13n + 8
C. 8n - 13
D. x + 91

Solutions
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Step: 1
Let n be a number.
Step: 2
13 more than 8 times a number = 8n + 13.
  [Write the expression.]
Step: 3
So, the variable expression for the phrase is 8n + 13.
Correct Answer is :   8n + 13
Q10Which of the following is equivalent to 4x + 3?

A. 3 more than 4 times x
B. 7 times x
C. 4 more than 3 times x
D. 3 less than 4 times x

Solutions
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Step: 1
4x means 4 times x.
Step: 2
4x + 3 means 3 more than 4 times x.
Step: 3
So, ' 3 more than 4 times x ' is equivalent to 4x + 3 .
Correct Answer is :   3 more than 4 times x
Q11Which of the following is equivalent to 8v + u?
A. 8 less than product of v and u
B. v more than 8 times u
C. u more than 8 times v
D. product of v and u divided by 8

Solutions
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Step: 1
8v means 8 times v.
Step: 2
8v + u means u more than 8 times v.
Step: 3
So, ' u more than 8 times v ' is equivalent to 8v + u .
Correct Answer is :   u more than 8 times v
Q12Choose the mathematical expression for the verbal description.
Twice as long as s
A. 2 - s
B. 2s
C. s + 2
D. 2s

Solutions
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Step: 1
'Twice as long as s' means 'Two times s'.
Step: 2
Two times s is given by 2s.
Step: 3
So, 2s is the mathematical expression for 'Twice as long as s'.
Correct Answer is :   2s
Q13Which of the following is equivalent to pq -12?

A. Product of p and q decreased by 12
B. 12 more than product of p and q
C. p times product of 12 and q
D. 12 times product of p and q

Solutions
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Step: 1
In the given expression, pq means product of p and q.
Step: 2
pq -12 means product of p and q decreased by 12.
Step: 3
So, from the given options, 'Product of p and q decreased by 12' is equivalent to pq - 12.
Correct Answer is :   Product of p and q decreased by 12
Q14Which of the following phrases represents the expression 9x+ 7?
A. 9 less than a number and 7
B. the sum of a number and 7
C. 7 less than 9 times a number
D. sum of 9 times a number and 7

Solutions
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Step: 1
In the given expression 9x+ 7, 9 is multiplied by an unknown quantity x and added by 7
Step: 2
So, from the given options, 'sum of 9 times a number and 7' is the correct answer.
Correct Answer is :   sum of 9 times a number and 7

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