Solving Systems using Matrix Equations and Inverses…
# 1-5: Write a system of equations for each problem. THEN SOLVE THE SYSTEM!!!!!
1) You are planning a birthday party for your younger brother at a skating rink. The cost of
admission is $3.50 per adult and $2.25 per child, and there is a limit of 20 people. You have
$50 to spend. Determine you many adults and how many children you can invite.
2) A walkway lighting package includes a transformer, a certain length of wire, and a certain
number of lights on the wire. The price of each lighting package depends on the length of
wire and the number of lights on the wire.
Package A contains one transformer, 25 feet of wire, and 5 lights and costs $20
Package B contains one transformer, 50 feet of wire, and 15 lights and costs $35
Package C contains one transformer, 100 feet of wire, and 20 lights and costs $50
Find the cost of a transformer, the cost per foot of wire, and the cost of a light.
3) You have $20.75 to spend on picking 15 pounds of three different types of apples in an
orchard. The Red Rome apples cost $1.29 per pound, the Granny Smith apples cost $1.49
per pound, and the Empire apples cost $1.09 per pound. You want twice as many Granny
Smith apples as the other two kinds combined. How many pounds of each type of apples
should you buy?
4) A store has a sale on almonds, pecans, and walnuts. One pound of almonds, one pound of
pecans, and one pound of walnuts cost $12. Two pounds of almonds and three pounds of
pecans cost $16. Three pounds of pecans and two pounds of walnuts cost $24. Find the
price of a pound of each type of nut.
5) A coin bank holds nickels, dimes, and quarters. There are 45 coins in the bank and the
value of the coins is $4.75. The number of nickels is five more than the number of
quarters. Find the number of each type of coin in the bank.
Write the matrix equation then solve:
6)
w + 6x + 3y – 3z = 2
2w + 7x + y + 2z = 5
w + 5x + 3y – 3z = 3
-6x – 2y + 3z = 6