3x3 Word Problems

3x3 System Word Problems

PAP Algebra 2

Fill in the Blanks

A certain 18-hole golf course has par-3, par-4 and par-5 holes and there are twice as many par-4 holes as there are par-5 holes. How many holes of each type are there if a golfer has par on every hole for a score of 70? Write the system of equations. Let x=par-3 holes, y=par-4 holes, z=par-5 holes

If the following two equations are part of the system, what is the third equation of the system?

x+y+z=18

3x+4y+5z=70

Fill in the Blanks

Use RREF to solve the matrix from the previous problem

Use parenthesis around the triple, commas between numbers, and alphabetical order (_,_,_)

Multiple Select

A piggy bank contains only nickels, dimes and quarters. Given the following information, write a 3x3 system to determine how many of each type of coin are in the bank.n=#nickels, d=#dimes, q=#quarters

• The coins total $4.50.

• There are 32 coins in the bank.

• The number of nickels and dimes together is 8 more than the number of quarters.

Which of the following equations would be a part of the system? (select all that apply)

• n+d+q=4.50

• n+d+q=32

• .05n+.10d+.25q=32

• .05n+.10d+.25q=4.50

• n+d=8+q

Fill in the Blanks

Shown is the system of equations for the previous piggy bank problem, set the system into an augmented matrix form, then use RREF to solve the system.

Write the triple with parenthesis, commas between numbers, and in alphabetical order

(_,_,_)

Multiple Select

Write a 3x3 system, to determine three numbers that satisfy the following conditions:

• the sum of the three numbers is 2.

• the sum of the first number, 5 times the second number, and 5 times the third number is -10.

• the sum of the first number, double the second number, and triple the third number is -3.

Let a=#1, b=#2, c=#3 Which of the following equations would be part of the system? (select all that apply)

• a+5b=3c-10

• a+5b+5c=-10

• a+2b+3c=-3

• a+2b=3c-3

• a+b+c=2

Fill in the Blanks

Shown is the 3x3 system for the previous number problem, set up an augmented matrix and use RREF to determine a,b, and c. Write answer with parenthesis, comma in between answers, and alphabetical order (_,_,_)

Multiple Choice

Caleb placed $5,500 in three investments that pay an annual interest of 4%, 5% and 7%. He placed twice as much money in the 7% investment as he did in the 4% investment. His total interest for the year is $320. Using a 3x3 system, determine the amount of money Caleb placed in each of the three investments. Let:

a=investment @ 4%, b=investment @ 5%, c=investment @ 7% Which system of equations can be used to solve the problem?

Fill in the Blanks

Set up the system into an augmented matrix then use RREF to solve the system

Use parenthesis, commas, and alphabetical order

Poll

How do you feel about setting up and solving 3x3 word problems

• Completely confident

• Confident

• Want some more practice

• Need more practice