3.4 Problem Solving with Three-Variable Systems

Advanced Algebra
Name _______________________________________
HOMEWORK FOR LESSON 3.4 Day 2
LINEAR SYSTEMS
Period ______ Date ____________________________
3.4 Problem Solving with Three-Variable Systems
For each problem, define THREE VARIABLES for the three unknown quantities.
Then write a system of THREE EQUATIONS which models the given situation. DO NOT SOLVE.
COMPLETE THESE PROBLEMS ON A SEPARATE SHEET OF PAPER.
1.
Joe Patriot has a piggy-bank filled with nickels, dimes, and quarters
totaling $8.90. The piggy-bank contains 76 coins in all. The number of
dimes is equal to the sum of the number of nickels and quarters.
How many of each coin does he have?
2.
Moe, Larry, and Curly went to Del Taco. Moe bought three tacos, two
burritos, and one nacho and paid $9.50. Larry bought two tacos, two
burritos, and two nachos and paid $9.00. Curly bought six tacos, four
burritos and three nachos and paid $20.00. What is the individual cost
of each item?
3.
In last night’s Lakers basketball game, Kobe, Pau, and Derek combined
to score 80 points. Kobe scored ten more points than Pau. Pau scored
twice as much as Derek. How many points did each player score?
4.
The sum of the measures of the three angles in any triangle is 180
degrees. In triangle ABC the measure of angle A is twice the sum of the
measures of angles B and C. The measure of angle B is three times the
measure of angle C. What are the measures of the three angles?
5.
At Edwards Theatre last night, 155 tickets were sold for the new
movie. Adult tickets sold for $12, student tickets $8, and seniors $9,
bringing in $1580 total. The number of adult tickets sold was four
times the number of senior tickets. How many of each type of ticket
were sold?
6.
Yoda, Anakin, and Obi-Wan are combining their savings for a flight to
the Death Star. Together, they have $680. Anakin has saved $20 less
than Obi-Wan. Yoda has saved triple what the other two have saved
put together. How much has each contributed to the total savings?
SEE OTHER SIDE
COMPLETE THESE PROBLEMS ON A SEPARATE SHEET OF PAPER.
For each problem, define THREE VARIABLES for the three unknown quantities.
Then write and SOLVE a system of THREE EQUATIONS which models the given situation.
7.
Stanley collects comic books. In his collection, he has 220 comics of the Batman, Ironman,
and Spiderman titles. He has twenty more Spiderman comics than Ironman. The number of
Batman comics is the same as the number of Spiderman. How many of each does he have?
8.
At a pizza shop, two small pizzas, a liter of root beer, and a salad cost $14. One small pizza,
a liter of root beer, and three salads cost $15. Three small pizzas and a liter of root beer
cost $16. What is the cost of one small pizza? Of one liter of root beer? Of one salad?
9.
On Sunday, January 22, 2006, Kobe Bryant of the Los Angeles Lakers scored 81 points, by
making 46 baskets (a combination of 1-point free-throws, 2-points shots, and 3-pointers).
Kobe made three times as many 2-point shots as 3-pointers. How many of each type of
shot did Kobe make on that historic night?
10. Patty Patriot has 165 coins in her purse, comprised of pennies, nickels, and dimes. The
total value of these coins is $4.50. The number of pennies is twice the sum of the number
of nickels and dimes. How many of each type of coin does Patty have in her purse?
Advanced Algebra
HOMEWORK FOR LESSON 3.4 Day 2
LINEAR SYSTEMS
1.
2.
ANSWER SHEET
Joe Patriot has a piggy-bank filled with nickels, dimes, and quarters
totaling $8.90. The piggy-bank contains 76 coins in all. The number of
dimes is equal to the sum of the number of nickels and quarters.
How many of each coin does he have?
22 nickels, 38 dimes, and 16 quarters
Moe, Larry, and Curly went to Del Taco. Moe bought three tacos, two
burritos, and one nacho and paid $9.50. Larry bought two tacos, two
burritos, and two nachos and paid $9.00. Curly bought six tacos, four
burritos and three nachos and paid $20.00. What is the individual cost
of each item?
Taco $1.50, Burrito $2.00, and Nachos $1.00
3.
In last night’s Lakers basketball game, Kobe, Pau, and Derek combined
to score 80 points. Kobe scored ten more points than Pau. Pau scored
twice as much as Derek. How many points did each player score?
Kobe 38, Pau 28, and Derek 14 points
4.
The sum of the measures of the three angles in any triangle is 180
degrees. In triangle ABC the measure of angle A is twice the sum of the
measures of angles B and C. The measure of angle B is three times the
measure of angle C. What are the measures of the three angles?
A = 120°, B = 45°, C = 15°
5.
At Edwards Theatre last night, 155 tickets were sold for the new
movie. Adult tickets sold for $12, student tickets $8, and seniors $9,
bringing in $1580 total. The number of adult tickets sold was four
times the number of senior tickets. How many of each type of ticket
were sold?
80 adult tickets, 55 student tickets , and 20 senior tickets
6.
Yoda, Anakin, and Obi-Wan are combining their savings for a flight to
the Death Star. Together, they have $680. Anakin has saved $20 less
than Obi-Wan. Yoda has saved triple what the other two have saved
put together. How much has each contributed to the total savings?
Yoda $510, Anakin $75, Obi-Wan $95
7.
Stanley collects comic books. In his collection, he has 220 comics of the Batman, Ironman,
and Spiderman titles. He has twenty more Spiderman comics than Ironman. The number of
Batman comics is the same as the number of Spiderman. How many of each does he have?
80 Batman, 60 Ironman, 80 Spiderman
8.
At a pizza shop, two small pizzas, a liter of root beer, and a salad cost $14. One small pizza,
a liter of root beer, and three salads cost $15. Three small pizzas and a liter of root beer
cost $16. What is the cost of one small pizza? Of one liter of root beer? Of one salad?
Pizza $5, Root Beer $1, Salad $3
9.
On Sunday, January 22, 2006, Kobe Bryant of the Los Angeles Lakers scored 81 points, by
making 46 baskets (a combination of 1-point free-throws, 2-points shots, and 3-pointers).
Kobe made three times as many 2-point shots as 3-pointers. How many of each type of
shot did Kobe make on that historic night?
18 free-throws, 21 two-pointers, and 7 three-pointers
10. Patty Patriot has 165 coins in her purse, comprised of pennies, nickels, and dimes. The
total value of these coins is $4.50. The number of pennies is twice the sum of the number
of nickels and dimes. How many of each type of coin does Patty have in her purse?
110 pennies, 42 nickels, 13 dimes