Acc Algebra 1
Name: ____________________________________
Unit 5: L5.3
Date:
______________
Period: ________
NOTES # 3… Applications of Systems of Equations/Inequalities (CRQ)
Part 1: CLASSWORK… Constructed-Response.
1)
Mickey and Minnie go to Sheetz to buy pizza flavored Combos and boxes of Firecracker Popsicles. Mickey
buys 6 bags of Combos and 2 boxes of popsicles. He spends $22.50. Minnie buys one bag of Combos and 6
boxes of popsicles. She spends $25.00. Later, their dog, Pluto joins Mickey and Minnie and asks to buy one
bag of Combos and one box of popsicles from them. They need to work out how much he should pay.
A)
Mickey writes 6c  2 p  22.50 . If c stands for the cost of a bag of Combos and p stands for the
cost of a box of popsicles, what does the 22.50 in Mickey’s equation mean?
B)
Write a similar equation, using c and p , for the items Minnie bought.
C)
Use the two equations to figure out the price of a bag of combos, c , and the price of a box of
popsicles, p.
D)
Pluto has just $6.50. Does he have enough money to buy a bag of Combos and a box of popsicles?
Explain your answer.
2)
Jimmy Neutron tutors Chemistry after school but his job pays only $5 per hour. He has been offered another
job at Annie’s Water-Ice for $6 per hour. Because of school, his parents allow him to work at most 25 hours
per week. How many hours can Jimmy tutor Chemistry and work at Annie’s and still make at least $120 per
week?
A)
This information can be modeled with a system of linear inequalities. When t is the number of hours
worked tutoring Chemistry and A is the number of hours worked at Annie’s. Two of the inequalities
that act as restrictions concerning this situation are t  0 and A  0 . Explain why these two
inequalities serve as restrictions on the system of inequalities.
B)
Write two more inequalities to complete the system.
C)
Graph the solution set for the inequalities from part A and part B below. Let the number of hours
worked tutoring Chemistry represent the horizontal axis and the number of hours worked at Annie’s
represent the vertical axis. Shade the area that represents the solution set.
Label each axis and use a scale of 2 on each axis.
D)
Pick an ordered pair to represent a reasonable solution for the number of hours worked tutoring and
hours worked at the water-ice store.
3)
A coal barge on the Ohio River takes 2 hours to make a 24 mile trip downstream and 3 hours on the 24 mile
return trip. Let v be the speed of the boat in still water, and c be the speed of the current. The upstream
speed of the boat is v  c and the downstream boat speed is v  c .
A)
Write two equations, one for the upstream part of the trip and one for the downstream part of the
trip. (Hint: Use the distance formula d  r  t )
B)
Solve the equations in part A for the speed of the current. Round your answer to the nearest tenth of
a mile per hour. Show your work.
C)
How long would it take the boat to travel the 24 miles if there were no current? Round your answer
to the nearest tenth of an hour. Show your work.
4)
The Doylestown Taxi Company charges a flat fee of $5.00 plus 15¢ per mile. The Bucks County Cab Company
charges a flat fee of $10.00 plus 12¢ per mile.
A)
Write an equation that represents the total cost, c , of riding a Doylestown Taxi cab for m miles.
B)
Write an equation that represents the total cost, c , of riding in a Bucks County Cab taxi for m miles.
C)
Suppose the cost of renting a car from two different rental agencies is represented by the following
equations:
Ralph’s Rental: c  2d  50
Rentals'r'Us:
c  3d  35
Let c represent total cost and d represent the number of days. Find the number of days when the
cost of renting a car is the same for both agencies.
D)
If you want to rent a car for 12 days, which car rental agency would you choose from the system in
part C and why?
Part 2: HOMEWORK… Constructed-Response.
YT 1)
Charlie Brown and Lucy go to the movies. They each buy their own snacks at the concession stand. Charlie
Brown buys 4 orders of nachos and 3 large popcorns with extra butter. He spends $46.50. Lucy buys 2 orders
of nachos and 2 large popcorns with extra butter. She spends $27.00. Their friend, Snoopy, comes late to the
movie and asks Charlie Brown and Lucy if he can buy one order of nachos and one bag of large popcorn with
extra butter from them. They need to work out how much he should pay.
A)
Charlie Brown writes 4n  3 p  46.50 . If n stands for the cost of an order of nachos and p stands
for the cost of a large popcorn with extra butter, what does the 46.50 in Charlie Brown’s equation
mean?
B)
Write a similar equation, using n and p , for the items Lucy bought.
C)
Use the two equations to figure out the price of an order of nachos, n, and the price of a large
popcorn with extra butter, p.
D)
Snoopy has just $15.00. Does he have enough money to buy an order of nachos and one large
popcorn with extra butter? Explain your answer.
YT 2)
Miley Cyrus gives music lessons after her recording sessions but this job pays only $8 per hour. She has been
offered another job at Nat’s Pizza folding pizza boxes for $12 per hour. Because of her busy recording
schedule, her agent only lets her work at most 18 hours a week. How many hours can Miley Cyrus give music
lessons and work at Nat’s an still make at least $180 per week?
A)
This information can be modeled with a system of linear inequalities. When m is the number of hours
worked giving music lessons and N is the number of hours worked at Nat’s. Two of the inequalities
that act as restrictions concerning this situation are m  0 and N  0 . Explain why these two
inequalities serve as restrictions on the system of inequalities.
B)
Write two more inequalities to complete the system.
C)
Graph the solution set for the inequalities from part A and part B below. Let the number of hours
worked giving music lessons represent the horizontal axis and the number of hours worked at Nat’s
represent the vertical axis. Shade the area that represents the solution set.
Label each axis and use a scale of 2 on each axis.
D)
Pick an ordered pair to represent a reasonable solution for the number of hours giving music lessons
and hours worked folding pizza boxes.
YT 3)
A canoe travels 4 miles upstream in 1 hour. The return trip takes the canoe 1.5 hours. Let v be the speed of
the boat in still water, and c be the speed of the current. The upstream speed of the canoe is v  c and the
downstream canoe speed is v  c .
A)
Write two equations, one for the upstream part of the trip and one for the downstream part of the
trip. (Hint: Use the distance formula d  r  t )
B)
Solve the equations in part A for the speed of the current. Round your answer to the nearest tenth of
a mile per hour. Show your work.
C)
How long would it take the canoe to travel the 4 miles if there were no current? Round your answer
to the nearest tenth of an hour. Show your work.
YT 4)
Center City Taxi company charges a flat fee of $2.50 plus 25¢ per mile. The Philly Phab Cab company charges
a flat fee of $5.00 plus 10¢ per mile.
A)
Write an equation that represents the total cost, c , of riding a Center City Taxi cab for m miles.
B)
Write an equation that represents the total cost, c , of riding in a Philly Phab Cab taxi for m miles.
C)
Suppose the cost of renting a car from two different rental agencies is represented by the following
equations:
Latner Plus:
Cars and Stars:
c  5d  25
c  2d  40
Let c represent total cost and d represent the number of days. Find the number of days when the
cost of renting a car is the same for both agencies.
D)
If you want to rent a car for the entire month of March, which car rental agency would you choose
from the system in part C and why?