Concept explainers
a.
To determine graph and expression of the inequalities that describes this situation.
a.
Explanation of Solution
Given:
The price of gold is about $25 per gram
The price of silver is approximately $0.40 per gram
The total mass must be more than 10 g but less than 20g
The ring must contain at least 2 g of gold
The total cost of the gold and silver must be less than $90
Calculation for graph:
Let
The price of gold is about $25 per gram so cost is $
The price of silver is approximately $0.40 per gram so cost ofis $0.
Total cost is
The total mass must be more than 10 g but less than 20g
So,
The total cost of the gold and silver must be less than $90
Total cost is
So,
Converting all the equation in slope interception form
INEQUALITY I:
The slope is -1 & the y -intercept is 10.
The shaded area is above the dashed boundary line.
INEQUALITY II:
The slope is -1 & the y -intercept is 20.
The shaded area is below the dashed boundary line.
INEQUALITY III:
The slope is -62.5 & the y -intercept is 20.
The shaded area is below the dashed boundary line.
Graph:
Here,
The solution is the intersection of the shaded regions in yellow and in black boundary.
Interpretation:
Therefore, the graph can be use to determine graph and expression of the inequalities that describes this situation.
b.
To determinethe mass of the ring and the cost of the gold and silver.
b.
Answer to Problem 36PPE
Explanation of Solution
Given:
The price of gold is about $25 per gram
The price of silver is approximately $0.40 per gram
The total mass must be more than 10 g but less than 20g
The ring must contain at least 2 g of gold
The total cost of the gold and silver must be less than $90
Calculation for graph:
From the above expression,
Let value of
Values of x | Value of y | Mass |
2 | 15 | 17 |
Values of x | Value of y | Cost |
2 | 15 | 56 |
Now plotting the graph,
Graph:
Here,
The solution is the intersection of the shaded regions in yellow and in black boundary.
Interpretation:
Therefore,the mass of the ring and the cost of the gold and silver for 2gram of gold and 15gram of silver17gram and $56 respectively.
Chapter 6 Solutions
High School Math 2015 Common Core Algebra 1 Student Edition Grade 8/9
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