Honors Algebra 2
Solve the following systems:
3x  y  z  3
1.
x  y  2z  4
x  2y  z  4
4x  z  y  5
2.
x  y  z  5
2x  z 1  y
Name ____________________
Period ______
Use a variable to represent each unknown quantity and write a system of equations that can be used
to solve the problem. Solve each one using the calculator.
3. Derek works at the peanut shop wanted to mix almonds, peanut and cashews to make 130 pound
of a mixture that he is going to charge $3.00 per pound. Almonds, Derek’s favorite, cost $2.50 per
pound, peanuts, Kenton’s favorite, cost $1.50 per pound and cashews, Jared’s favorite other than
skittles, cost $4.00 per pound. If Derek wants to use twice as many peanuts as almonds, how many
pounds of each variety should be mixed?
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4. Mark can now go buy an ice cream cone because he has a piggy bank containing nickels, dimes
and quarters. In all, he has 22 coins with a total value of $2.55. The number of dimes is 4 less than
the number of nickels and quarters put together. Find the number of dimes, nickels and quarters in
Mark’s piggy bank.
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5. A box of wood pieces contains wood cut into triangular, square and pentagonal shapes. There are
80 pieces of wood in the box and the pieces have a total of 290 sides. If there are 10 more
triangular pieces that square pieces, find the number of each shape in the package.
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6. A store sells three items for the regular price on Monday. The total of the regular prices of the
three is $48. On Tuesday, the store sells item A for
and item C for
1
3
1
the regular price, item B for the regular price,
2
the regular price. The cost of buying the three items is $31. On Wednesday, the
store sells item A for
1
1
the regular price, item B for the regular price and item C for the regular
2
4
price. On Wednesday the cost of the three items was $28.
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7. Solve
3  42  y 
1
 2 y  5
2