Answer:
1) There were 34 $3,000 investors and 26 $6,000 investors.
2) There are 26 nickels and 44 dimes in the jar.
3) 1600 sodas and 1400 hot dogs were sold.
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 $3,000 or $6,000. If the partnership raised $258,000, then how many investors contributed $3,000 and how many contributed $6,000?
x is the number of investors that contributed 3,000.
y is the number of investors that contributed 6,000.
Building the system:
There are 60 investors. So:
In all, the partnership raised $258,000. So:
Simplifying by 3000, we have:
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, then add 1) and 2), so x is canceled.
Now we get back to equation 1), and find x
There were 34 $3,000 investors and 26 $6,000 investors.
2) A jar contains 70 nickels and dimes worth $5.70. 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 70 coins. So:
They are worth $5.70. So:
Solving the system:
I am going to divide 1) by -10, so we can add and cancel y:
*(-100)
Now:
There are 26 nickels and 44 dimes in the jar.
3) The concession stand at an ice hockey rink had receipts of $7400 from selling a total of 3000 sodas and hot dogs. If each soda sold for $2 and each hot dog sold for $3, how many of each were sold?
x is the nuber of sodas and y is the number of hot dogs.
Building the system:
3000 items were sold. So:
$7,4000 was the total price of these items. So:
Solving the system:
I am going to multiply 1) by -2, so we can cancel x
Now, going back to 1)
1600 sodas and 1400 hot dogs were sold.