Question

1. 8 times luke’s speed
2. the product of 4 and a
3. 7 more than lou’s weight
4. 9 less than c
5. 4 less than d
6. 6 increased by q
7. 11 increased by z
8. the difference of m and n
9. t subtracted from p
10. x less than y
11. 2 less than lorrie’s age
12. x divided by w
13. the quotient of two numbers
14. the sum of the box’s length and height
15. the sum of d and f

Explanation:

Let's solve each problem by translating the verbal expressions into algebraic expressions:

Problem 32: 8 times Luke’s speed

Let Luke's speed be \( s \). "8 times" means multiplication.
Expression: \( 8s \)

Problem 33: The product of 4 and \( a \)

"Product" means multiplication.
Expression: \( 4 \times a = 4a \)

Problem 34: 7 more than Lou’s weight

Let Lou's weight be \( w \). "7 more than" means addition.
Expression: \( w + 7 \)

Problem 35: 9 less than \( c \)

"9 less than" means subtraction (subtract 9 from \( c \)).
Expression: \( c - 9 \)

Problem 36: 4 less than \( d \)

"4 less than" means subtraction (subtract 4 from \( d \)).
Expression: \( d - 4 \)

Problem 37: 6 increased by \( q \)

"Increased by" means addition.
Expression: \( 6 + q \)

Problem 38: 11 increased by \( z \)

"Increased by" means addition.
Expression: \( 11 + z \)

Problem 39: The difference of \( m \) and \( n \)

"Difference" means subtraction (subtract \( n \) from \( m \)).
Expression: \( m - n \)

Problem 40: \( t \) subtracted from \( p \)

"Subtracted from" means \( p - t \) (subtract \( t \) from \( p \)).
Expression: \( p - t \)

Problem 41: \( x \) less than \( y \)

"\( x \) less than" means \( y - x \) (subtract \( x \) from \( y \)).
Expression: \( y - x \)

Problem 42: 2 less than Lorrie’s age

Let Lorrie's age be \( a \). "2 less than" means subtraction.
Expression: \( a - 2 \)

Problem 43: \( x \) divided by \( w \)

"Divided by" means division.
Expression: \( \frac{x}{w} \)

Problem 44: The quotient of two numbers

Let the two numbers be \( a \) and \( b \) ( \( b
eq 0 \) ). "Quotient" means division.
Expression: \( \frac{a}{b} \)

Problem 45: The sum of the box’s length and height

Let length be \( l \) and height be \( h \). "Sum" means addition.
Expression: \( l + h \)

Problem 46: The sum of \( d \) and \( f \)

"Sum" means addition.
Expression: \( d + f \)

Final Answers:

1. \( \boldsymbol{8s} \)
2. \( \boldsymbol{4a} \)
3. \( \boldsymbol{w + 7} \) (where \( w \) = Lou’s weight)
4. \( \boldsymbol{c - 9} \)
5. \( \boldsymbol{d - 4} \)
6. \( \boldsymbol{6 + q} \)
7. \( \boldsymbol{11 + z} \)
8. \( \boldsymbol{m - n} \)
9. \( \boldsymbol{p - t} \)
10. \( \boldsymbol{y - x} \)
11. \( \boldsymbol{a - 2} \) (where \( a \) = Lorrie’s age)
12. \( \boldsymbol{\frac{x}{w}} \)
13. \( \boldsymbol{\frac{a}{b}} \) (where \( a, b \) are the two numbers, \( b

eq 0 \))

1. \( \boldsymbol{l + h} \) (where \( l \) = length, \( h \) = height)
2. \( \boldsymbol{d + f} \)

Answer:

Let's solve each problem by translating the verbal expressions into algebraic expressions:

Problem 32: 8 times Luke’s speed

Let Luke's speed be \( s \). "8 times" means multiplication.
Expression: \( 8s \)

Problem 33: The product of 4 and \( a \)

"Product" means multiplication.
Expression: \( 4 \times a = 4a \)

Problem 34: 7 more than Lou’s weight

Let Lou's weight be \( w \). "7 more than" means addition.
Expression: \( w + 7 \)

Problem 35: 9 less than \( c \)

"9 less than" means subtraction (subtract 9 from \( c \)).
Expression: \( c - 9 \)

Problem 36: 4 less than \( d \)

"4 less than" means subtraction (subtract 4 from \( d \)).
Expression: \( d - 4 \)

Problem 37: 6 increased by \( q \)

"Increased by" means addition.
Expression: \( 6 + q \)

Problem 38: 11 increased by \( z \)

"Increased by" means addition.
Expression: \( 11 + z \)

Problem 39: The difference of \( m \) and \( n \)

"Difference" means subtraction (subtract \( n \) from \( m \)).
Expression: \( m - n \)

Problem 40: \( t \) subtracted from \( p \)

"Subtracted from" means \( p - t \) (subtract \( t \) from \( p \)).
Expression: \( p - t \)

Problem 41: \( x \) less than \( y \)

"\( x \) less than" means \( y - x \) (subtract \( x \) from \( y \)).
Expression: \( y - x \)

Problem 42: 2 less than Lorrie’s age

Let Lorrie's age be \( a \). "2 less than" means subtraction.
Expression: \( a - 2 \)

Problem 43: \( x \) divided by \( w \)

"Divided by" means division.
Expression: \( \frac{x}{w} \)

Problem 44: The quotient of two numbers

Let the two numbers be \( a \) and \( b \) ( \( b
eq 0 \) ). "Quotient" means division.
Expression: \( \frac{a}{b} \)

Problem 45: The sum of the box’s length and height

Let length be \( l \) and height be \( h \). "Sum" means addition.
Expression: \( l + h \)

Problem 46: The sum of \( d \) and \( f \)

"Sum" means addition.
Expression: \( d + f \)

Final Answers:

1. \( \boldsymbol{8s} \)
2. \( \boldsymbol{4a} \)
3. \( \boldsymbol{w + 7} \) (where \( w \) = Lou’s weight)
4. \( \boldsymbol{c - 9} \)
5. \( \boldsymbol{d - 4} \)
6. \( \boldsymbol{6 + q} \)
7. \( \boldsymbol{11 + z} \)
8. \( \boldsymbol{m - n} \)
9. \( \boldsymbol{p - t} \)
10. \( \boldsymbol{y - x} \)
11. \( \boldsymbol{a - 2} \) (where \( a \) = Lorrie’s age)
12. \( \boldsymbol{\frac{x}{w}} \)
13. \( \boldsymbol{\frac{a}{b}} \) (where \( a, b \) are the two numbers, \( b

eq 0 \))

1. \( \boldsymbol{l + h} \) (where \( l \) = length, \( h \) = height)
2. \( \boldsymbol{d + f} \)