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Tom paid d cents for a notebook and 5d + 30 cents for a pen. Write in words each given algebraic expression. Describe a possible domain for this variable.

a) d cents for a notebook, (5d + 30) cents for a pen
b) 5d + 30 cents for a notebook, (d) cents for a pen
c) d dollars for a notebook, (5d + 30) dollars for a pen
d) 5d + 30 dollars for a notebook, (d) dollars for a pen

User Derdc
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Final answer:

Tom's expenses for notebooks and pens are represented using algebraic expressions with the variable 'd' representing the cost in cents or dollars. Each expression outlines a relationship between the item's cost and the variable. The domain for 'd' is likely the set of positive integers.

Step-by-step explanation:

Tom's expenses can be represented algebraically, expressing both monetary value and the relationship between the costs of different items. For the given expressions:

  • a) In words, 'd cents for a notebook' means that the cost of a notebook is directly proportional to the value of d. The expression '(5d + 30) cents for a pen' represents the cost of a pen as five times the value of d plus an additional 30 cents.
  • b) '5d + 30 cents for a notebook' implies that the notebook's cost is five times the value of d plus 30 cents whereas '(d) cents for a pen' suggests the pen costs d cents.
  • c) In terms of dollars, 'd dollars for a notebook' translates to the notebook costing d dollars. '5d + 30 dollars for a pen' indicates the pen costs five times d plus an additional 30 dollars.
  • d) '5d + 30 dollars for a notebook' means the notebook is five times more expensive than some unit d, plus 30 dollars and '(d) dollars for a pen' means the pen costs d dollars.

The domain for the variable d in this context would likely be the set of positive integers since it is unrealistic to have a fractional cent value and one typically does not deal with negative costs in this scenario.

User Sayan Pathak
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