Answer:
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Answer:
US$ 132.45
Step-by-step explanation:
See attachment for the missing table.
Given:
Richard’s checking account balance at the beginning of the week = $57.34
<u>Richard’s account balance at the end of the week from the given table:</u>
Deposits of the week = US$ 163.75
Expenses of the week = Groceries + Credit card bill + Gas
Expenses of the week = 25.37 + 50 + 13.27
Expenses of the week = US$ 88.64
Richard’s account balance at the end of the week = Richard’s checking account balance at the beginning of the week + Deposits of the week - Expenses of the week
Replacing with the real values:
Richard’s account balance at the end of the week = 57.34 + 163.75 - 88.64
=US$ 132.4
Answer:
Between 150 and 450
Step-by-step explanation:
We are going to find the number by resolving a system of linear equations.
First we write the system equations :
Where C : children, S : students and A : adults
The equation represents the ''full attendance''
The second equation :
This equation represents the totaled receipts.
The system :
has the following associated matrix :
By performing elementary matrix operations we find that the matrix is equivalent to
The new system :
Working with the equations :
Our solution vector is :
For example :
If 0 adults attended ⇒ A = 0
This verify the totaled receipts equation :
150($3)+600($5) = $ 3450
A ≥ 0 ⇒ If A = 0 ⇒ C = 150
C = 150 is the minimum children attendance
From the equation :
S ≥0
600 - 2A ≥ 0
600 ≥ 2A
300≥ A
A is restricted to the interval [ 0, 300]
When A = 0 ⇒ C = 150
When A = 300 ⇒C = 150 + A = 150 + 300 = 450
Children ∈ [ 150,450]
With C being an integer number (including 0)
Also S and A are integer numbers (including 0)