(a)
To choose: Two variables that represent the number of each coins.
(a)
Answer to Problem 7P
The variables representing the number of coins coins are d and n.
Explanation of Solution
Given information: A box contains nickels, dimes and quarters. There are three more dimesthan the quarters.
Calculation:
(b)
To write: An open sentence relating to the variables.
(b)
Answer to Problem 7P
The open sentence is
Explanation of Solution
Given information: A box contains nickels, dimes and quarters worth $2.00. There are three more dimes than the quarters.
Calculation:
There are d dimes,
There are d dimes, their worth is,
There are
There are n nickels, their worth is,
Total worth of these coins is,
It is given that the total worth is equal to
(b)
To write: An open sentence relating to the variables.
(b)
Answer to Problem 7P
The open sentence is
Explanation of Solution
Given information: A box contains nickels, dimes and quarters worth $2.00. There are three more dimes than the quarters.
Calculation:
There are d dimes,
There are d dimes, their worth is,
There are
There are n nickels, their worth is,
Total worth of these coins is,
It is given that the total worth is equal to
(c)
To solve: The open system for integral values.
(c)
Answer to Problem 7P
The only possible integral pairs are
Explanation of Solution
Given information:The open sentence is
Calculation:
The open sentence is
The variable n in terms of dis ,
Choose
Choose
Choose
Choose
Remaining all other combinations yield negative number of coins. Since, the number of coins can always be positive all such possibilities are directly neglected.
Therefore, the only possible integral pairs are,
(c)
To solve: The open system for integral values.
(c)
Answer to Problem 7P
The only possible integral pairs are
Explanation of Solution
Given information:The open sentence is
Calculation:
The open sentence is
The variable n in terms of dis ,
Choose
Choose
Choose
Choose
Remaining all other combinations yield negative number of coins. Since, the number of coins can always be positive all such possibilities are directly neglected.
Therefore, the only possible integral pairs are,
Chapter 3 Solutions
Algebra and Trigonometry: Structure and Method, Book 2
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