Andros has an oil fired heating system. In a 30-day period he used a full tank of oil at a constant rate per day. At a different
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1)Define the variables you will use in your model.
Let
x------->total pounds of the fruit
y-------> the total number of granola bars
TC----> total cost
Tf------> total cost of the fruit
Tg----> total cost of the granola bars
2) Write an inequality representing the total cost of your purchase. (3 points)
a. Each pound of fruit costs $4. Write an expression that shows the total cost of the fruit. Use the variable you identified in question 1
Tf=4*x
b. Each granola bar costs $1. Write an expression that shows the total cost of the granola bars. Use the variable you identified in question 1.
Tg=1*y--------> Tg=y
c. Combine the expressions from parts a and b to write an expression for the total cost. Then use this expression to write an inequality that compares the total cost with the amount you have to spend.
TC=Tf+Tg
TC=4*x+y
inequality------->
3. Write the inequality that models the number of granola bars you need to buy.
You need at least 10 granola bars
so
4. Describe in words what each of your inequalities means
inequality 1
the total cost of fruits plus the total cost of granola bars must be less than or equal to 48 dollars
inequality 2
5. Graph your system of inequalities.
using a graph tool
see the attached figure
6. Identify one point on the graph that represents a viable solution to the problem, and then identify one point that does not represent a viable solution.
Let
A-------> one point on the graph that represents a viable solution
B-------> one point on the graph that does not represent a viable solution
A(4,20)
x=4-------> total pounds of the fruit
y=20------> the total number of granola bars
check point A
substitute the values of x and y in the inequality 1
-------> is ok
substitute the values of x and y in the inequality 2
--------> is ok
the point A represents a viable solution, because satisfies both inequalities
B(10,30)
x=10-------> total pounds of the fruit
y=30------> the total number of granola bars
check point B
substitute the values of x and y in the inequality 1
-------> is not a viable solution
substitute the values of x and y in the inequality 2
--------> is ok
the point B is not a viable solution because does not satisfy the inequality 1
Answer:
The inequality to determine the number of days, s, Darcie can skip crocheting and still meet her goal can be given as:
Step-by-step explanation:
The complete question is:
Darcie wants to crochet a minimum of 3 blankets to donate to a homeless shelter. Darcie crochets at a rate of 1/15 of a blanket per day. She has 60 days until when she wants to donate the blankets, but she also wants to skip crocheting some days so she can volunteer in other ways. Write an inequality to determine the number of days, s, Darcie can skip crocheting and still meet her goal.
Solution:
Given:
Darcie wants to crochet a minimum of 3 blankets to donate.
Rate at which she crochet = of a blanket per day.
Maximum number of days she has = 60.
To find the number of days Dancie can skip out of 60 days and still reach her goal.
Let represent the number of days she can skip.
Number of days left to crochet = days
At rate of of a blanket per day, number of blankets Dancie can corchet in
days can be given as :
⇒
Simplifying using distribution.
⇒
⇒
Dancie needs to crochet a minimum of 3 blankets to reach her goal.
Thus, the inequality can be given as:
Solving the inequality for
Subtracting 4 both sides.
Multiplying both sides by -15.
[On multiplying by a negative number the sign of inequality reverse]
∴
Thus, Dancie can skip a maximum of 15 days.