WHRHS
2011-2012
Unit 12 – Solving Systems of Equations & Inequalities
Algebra 2A
Unit 12 – Day G – Systems of Equations - Word Problems
Kuta Software - Infinite Algebra 2
1) The school that Lisa goes to is selling tickets to the annual talent show. On the first day of ticket sales the school sold 4
senior citizen tickets and 5 student tickets for a total of $102. The school took in $126 on the second day by selling 7
senior citizen tickets and 5 student tickets. What is the price each of one senior citizen ticket and one student ticket?
2) Flying with the wind a plane went 183 km/h. Flying into the same wind the plane only went 141 km/h. Find the speed
of the plane in still air and the speed of the wind.
3) Castel and Gabriella are selling pies for a school fundraiser. Customers can buy apple pies and lemon meringue pies.
Castel sold 6 apple pies and 4 lemon meringue pies for a total of $80. Gabriella sold 6 apple pies and 5 lemon meringue
pies for a total of $94. What is the cost each of one apple pie and one lemon meringue pie?
7) A plane traveled 580 miles to Ankara and back. The trip there was with the wind. It took 5 hours. The trip back was
into the wind. The trip back took 10 hours. Find the speed of the plane in still air and the speed of the wind.
9) The local amusement park is a popular field trip destination. This year the senior class at High School A and the senior
class at High School B both planned trips there. The senior class at High School A rented and filled 16 vans and 8 buses
with 752 students. High School B rented and filled 5 vans and 5 buses with 380 students. Each van and each bus carried
the same number of students. How many students can a van carry? How many students can a bus carry?
WHRHS
2011-2012
Unit 12 – Solving Systems of Equations & Inequalities
Algebra 2A
More System of Equations – Word Problems:
1. The sum of two numbers is 42. One number is 3 less than 4 times the other number. What are the numbers?
2. Miss Lee has 24 coins consisting of nickels and quarters. The total value of the coins is $3.00. How many of each kind
does Miss Lee have?
3. Pavilion seats for the concert sold at $14.00 and lawn seats sold at $11.75. The total receipts from the sale of 942
tickets were $12,402.75. How many of each type of ticket were sold?
4. An airplane traveled 2660 miles in 3.5 hours with a tail wind. The return trip took 3.8 hours with a head wind. What
was the speed of the airplane in still air? What was the speed of the wind?
5. A helicopter flew 180 miles in 1.5 hours with a tail wind. The return trip took 2 hours with a head wind. What was
the speed of the helicopter in still air? What was the speed of the wind?
6. When the digits of a two-digit number are reversed, the resulting number is 54 less than the original number. The
tens digit of the original number is 4 times the units digit. What is the original number?
7. When the digits of a two-digit number are reversed, the resulting number is 63 more than the original number. The
units digit of the original number is one more than 4 times the tens digit. What is the original number?
WHRHS
2011-2012
Unit 12 – Solving Systems of Equations & Inequalities
Algebra 2A
8. 5 Lbs. of Almonds and 2 Lbs. of Raisins cost $18.93, while 3 Lbs. of Almonds and 4 Lbs. of Raisins cost $14.97. Find
the cost of a Lb. of each.
9. Twice one number is 20 more than another number. One fourth the first number is 2 less than one fourth the second
number. Find the numbers.
10. One third of the sum of two numbers is -1/3, while one third of their difference is 3. Find the numbers.
11. Martha earns $5.50 per hour and Joan earns $6.50 per hour. Together they worked a total of 45 hours one week
and earned a total of $266.50. How many hours did each work?
12. For some long distance calls, a fixed amount is charged for the first three minutes, and a fixed rate is charged for
each additional minute. If the charge for a 15 minute call from New York to Chicago is $2.94, and the charge for a 10
minute call is $1.99, find the fixed amount that is charged for the first 3 minutes and the fixed rate that is charged for
each additional minute.
13. Three dozen eggs and five loaves of bread cost $6.10; four dozen eggs and two loaves of bread cost $5.10. Find the
prices for a dozen eggs and a loaf of bread.
WHRHS
2011-2012
Unit 12 – Solving Systems of Equations & Inequalities
Algebra 2A
14. Flying with the wind, an airplane can travel 1500 km in 2.5 hours, but flying against the wind, the plane requires 0.5
more hours to make the return trip. Find the wind speed and air speed.
15. The tens’ digit exceeds the units’ digit by one. The difference between the original number and the number
represented when the digits are reversed is equal to the tens’ digit of the original number.
16. The units’ digit is one more than twice the tens’ digit. The sum of the original number and the number represented
when the digits are reversed is 77.
17. A boat travels 64 miles downstream in 2 hours and returns 54 miles upstream in 3 hours. What is the rate of the
current, and the rate of the boat in still water?
18. Find a 3 digit number such that the sum of the digits is 12, twice the hundreds digit equals the sum of the other 2
digits, and the units digit is 2 more than the sum of the tens & hundreds digit.
WHRHS
2011-2012
Unit 12 – Solving Systems of Equations & Inequalities
Algebra 2A
Answer Key for Unit 12 Day G Word Problems:
Kuta Software Word Problems:
1. Senior ticket = $8 & Student ticket = $14
2. Plane = 162 km/hr & Wind = 21 km/hr
3. Apple Pie = $4 & Lemon Meringue Pie = $14
4. Plane = 87 mph & Wind = 29 mph
5. Van = 18 & Bus = 58
More Word Problems:
1. x = 9 & y = 33
10. y = -5 & x = 4
2. q = 9 & n = 15
11. J = 19 hrs & M = 26 hrs
3. L = 349 & P = 593
12. y = $.19 & x = $.66 per minute
4. Wind = 30 mph & Rate = 730 mph
13. l = y = $.65 & d = x = $.95
5. Wind = 15 mph & Rate = 105 mph
14. Wind = 50 km/hr & Air Rate = 550 km/hr
6. u = 2 & t = 8 orig # = 82
15. u = 8 & t = 9 orig # = 98
7. t = 2 & u = 9 orig # = 29
16. t = 2 & u = 5 orig # = 25
8. Almonds = $3.27 & Raisins = $1.29
17. Current = 7 mph & Boat Rate = 25 mph
9. y = 36 & x = 28
18. u = 7 & t = 1 & h = 4 orig # = 417