Concept explainers
(a)
To find:. The proportional situation between Isabel savings and her sister savings by showing the first six weeks saving for each girl in the tables.
(a)
Answer to Problem 14IP
The money saved by Isabel is not proportional to the number of weeks and the money saved by her sister is proportional to the number of weeks.
Explanation of Solution
Given information: The cost saved by Isabel per week is
Two quantities in which the ratio or rate is constant, are to be said proportional and if the rates are not constant, then the quantities are said to be non-proportional. The constant ratio which is defining whether the two quantities are said to be proportional or not is known as constant of proportionality.
The cost saved by Isabel per week is:
To find cost for
To find cost for
To find cost for
To find cost for
To find cost for
The table showing rate of cost to number of weeks is shown below:
Number of weeks | ||||||
Cost ( |
The set to be said proportional, if cost to number of weeks have equivalent rates. So, the expression for equivalent rates is:
Therefore, from the above expression it is clear that the cost of the savings is proportional to the number of the weeks and constant of proportionality is
The cost saved by Isabel sister per week is:
To find cost for
To find cost for
To find cost for
To find cost for
To find cost for
The table showing rate of cost to number of weeks is shown below:
Number of weeks | ||||||
Cost ( |
The set to be said proportional, if cost to number of weeks have equivalent rates. So, the expression for equivalent rates is:
Therefore, from the above expression it is clear that the cost of the savings is proportional to the number of the weeks and thus no constant of proportionality.
(b)
To find: The equation showing the number of weeks and saving cost proportional relationship.
(b)
Answer to Problem 14IP
The equation showing the number of weeks and saving cost of Isabel proportional relationship is
Explanation of Solution
Given information:The cost saved by Isabel per week is
Calculation:
The constant of proportionality of Isabel is:
The expression of Proportional relationships in equation form is:
Here, the constant of proportionality is
The amount of savings to the number of weeks, in which the number of weeks is
Substitute
Therefore, the equation showing the number of weeks and saving cost of Isabel proportional relationshipis
The constant of proportionality for Isabel’s sister is:
The expression of Proportional relationships for Isabel’s sister in equation form is:
Here, the constant of proportionality is
Substitute
Therefore, the equation showing the number of weeks and saving cost of Isabel sister’s proportional relationshipis
(c)
To explain: The comparison of Graph A and Graph B.
(c)
Explanation of Solution
Given information: The savings per week of Isabel and Isabel’s sister is shown in the following graph
Graph:
Interpretation:
To determine whether the relationship is proportional or not, the graph must be passing through straight line through the origin.
In the above graph A,
In the above graph B,
Chapter 5 Solutions
Glencoe Math Accelerated, Student Edition
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