Answer:
1) There were 33 $4,000 investors and 27 $8,000 investors.
2) The solution in x = 4, y = 9.
3) There were 24 nickels and 56 dimes.
Step-by-step explanation:
1) A lawyer has found 60 investors for a limited partnership to purchase an inner-city apartment building, with each contributing either $4,000 or $8,000. If the partnership raised $348,000, then how many investors contributed $4,000 and how many contributed $8,000?
I am going to say that:
x is the number of investors that contributed 4,000.
y is the number of investors that contributed 8,000.
Building the system:
There are 60 investors. So:
In all, the partnership raised $348,000. So:
I am going to simplify by 4000. So:
Solving the system:
The elimination method is a method in which we can transform the system such that one variable can be canceled by addition. So:
I am going to multiply 1) by -1. So we have
By addition, the x are going to cancel each other
For x:
There were 33 $4,000 investors and 27 $8,000 investors.
2) Solve the system by row-reducing the corresponding augmented matrix.
This system has the following augmented matrix:
To help the row reducing, i am going to swap the first with the second line:
So we have:
Now, reducing the first column.
So we have:
Now we do:
And the matrix is:
Now to reduce the second column, we do:
.
So the solution is:
x = 4, y = 9.
3) A jar contains 80 nickels and dimes worth $6.80. How many of each kind of coin are in the jar?
I am going to say that x is the number of nickels and y is the number of dimes.
Each nickel is worth 5 cents and each dime is worth 10 cents.
Building the system:
There are 80 coins in all:
They are worth $6.80. So:
Solving the system:
I am going to divide 1) by -10, so we can cancel y. So:
Adding:
*(-100)
Also
There were 24 nickels and 56 dimes.