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Algebra II PAP
Applications
Name______________________________________
Write a system of equations for the following situations. Define your variables and then write a matrix
equation. Solve each system using the calculator (or using an algebraic method). Clearly state the meaning
of your solutions.
ex. You and your sister decide to combine your weekly overtime earnings to buy a birthday gift for your
mother. Your overtime rate is $18 per hour and your sister’s overtime rate is $24 per hour. The total
amount earned for the gift was $288. If you worked two more hours of overtime than your sister, how
many hours did each of you work?
1. The sum of two numbers is 44 and their difference is 20. What are the numbers?
2. The sum of the digits of a two-digit number is 10. If the unit’s digit is 11 less than twice the ten’s digit, what
is the number?
3. Ms. Martin’s coin purse contains only dimes and quarters. The total value of the coins is $6.25. If the
number of dimes and quarters were reversed, the coins would value $5.65. How many dimes are there in her
purse?
4. Coffee worth $1.05 per pound is mixed with coffee worth 85 cents per pound to obtain twenty pounds of a
mixture worth 90 cents per pound. How many pounds of each type are used?
5. You have $33 to spend on 24 balloons. Birthday balloons cost $1.50 each, congratulations balloons cost
$1.00 each, and get well soon balloons cost $2.00 each. You want twice as many birthday balloons as the
other two kinds combined. Which system of equations could be used to represent this situation?
6. At an entertainment store, 2 music CDs, 3 movie DVDs, and 1 movie VHS cost $96; 3 music CDs, 3 movie
DVDs, and 2 movie VHSs cost $123; and 4 music CDs, 1 movie DVD, and 2 movie VHSs cost $102. What is the
cost of one CD? Of one DVD? Of one movie VHS?
7. A collection of nickels, dimes, and quarters totals $3.85. There are 45 coins in the collection. If there are 4
times as many dimes as quarters, find the number of nickels, dimes, and quarters in the collection.
8-10 Write a quadratic function in standard form for the parabola that passes through the given points.
8. (-1,-1), (1,11), (3,7)
9. (-6,-1), (-3,-4), (3,8)
10. (-6,29), (-4,12), (2,-3)
11. Create your own application problem! It can be a 2x2 or 3x3. Make sure to set up your system for your
problem but do not solve.