Formulate the situation as a system of two linear equations in two variables. be sure to state clearly the meaning of your x- and y-variables. solve the system by the elimination method. be sure to state your final answer in terms of the original question.
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?
x = $4,000 investors
y =
$8,000 investors
solve the system by row-reducing the corresponding augmented matrix. (enter your answers as a comma-separated list. if the system is inconsistent, enter inconsistent. if the system is dependent, enter dependent.)
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2x + y = 17
x + y = 13
the situation as a system of two linear equations in two variables. be sure to state clearly the meaning of your x- and y-variables. solve the system by the elimination method. be sure to state your final answer in terms of the original question.
a jar contains 80 nickels and dimes worth $6.80. how many of each kind of coin are in the jar?
x = nickels
y = dimes

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.