Day 2 Algebra Student1

Name: ____________________________ Date: _________________Per:____
Student Page
Algebra/Day 2
Systems of Equations
1 Janice is going on vacation and needs to leave her dog at a kennel. Nguyen’s Kennel charges
$15 per day plus $20 for a processing fee. The Pup Palace Kennel charges $12 per day, and has
a $35 processing fee. After how many days is the Pup Palace Kennel cheaper than Nguyen’s
Kennel?
A The Pup Palace Kennel is always cheaper than Nguyen’s Kennel.
B The Pup Palace Kennel is never cheaper than Nguyen’s Kennel.
C The Pup Palace Kennel is cheaper than Nguyen’s Kennel after 15 days.
D The Pup Palace Kennel is cheaper than Nguyen’s Kennel after 5 days.
2 Solve
A
B
by using elimination. Express your answer as an ordered pair.
(5, 0)
(5, 17.5)
C
D
(5, 22.5)
(5, 40)
3 The sum of the digits of a two-digit number is 8. If the number is multiplied by 4, the result is 104.
Write and solve a system of equations. Find the number.
C
A
The number is 35.
The number is 18.
D
B
The number is 17.
The number is 26.
4 Lauren is comparing the cost of long distance calling cards. To use card A, it cost $0.50 to
connect and then $0.05 per minute. To use card B, it costs $0.20 to connect and then $0.08 per
minute.
a. Write an equation for the cost of connect and the cost per minute for each card.
b. For what number of minutes does it cost the same amount to use each card for a
single call?
In the answer box provided, with words, graphs, tables or equations, show your solution
to the problem. Only work within the answer box will be scored.
Name: ____________________________ Date: _________________Per:____
Student Page
Algebra/Day 2
Systems of Equations
5 An ice skating arena charges an admission fee for each child plus a rental fee for each pair of ice
skates. John paid the admission fees for his six nephews and rented five pairs of ice skates. He
was charged $32.00. Juanita paid the admission fees for her seven grandchildren and rented five
pairs of ice skates. She was charged $35.25. What is the admission fee? What is the rental fee
for a pair of skates?
A admission fee: $3.25
C admission fee: $3.00
skate rental fee: $2.50
skate rental fee: $2.00
B admission fee: $3.50
D admission fee: $4.00
skate rental fee: $3.00
skate rental fee: $3.50
6 Mrs. Huang operates a soybean farm. She buys many supplies in bulk. Often the bulk products
need to be custom mixed before Mrs. Huang can use them. To apply herbicide to a large field she
must mix a solution of 67% herbicide with a solution of 46% herbicide to form 42 liters of a 55%
solution. How much of the 67% solution must she use?
A 23 L
B 18 L
C 34 L
D 35 L
7 You decide to market your own custom computer software. You must invest $3,255 for computer
hardware, and spend $2.90 to buy and package each disk. If each program sells for $13.75, how
many copies must you sell to break even?
A 196 copies
B 301 copies
C 300 copies
D 195 copies
8 At the local ballpark, the team charges $5 for each ticket and expects to make $1,400 in
concessions. The team must pay its players $2,000 and pay all other workers $1,600. Each fan
gets a free bat that costs the team $3 per bat. How many tickets must be sold to break even?
A 440
B 1,100
C 2,500
D 275
9 Brad is a farmer. He feeds his hogs 12 pounds of feed per day and has 70 pounds of feed in his
barn. Cliff is also a farmer. He feeds his hogs 15 pounds of feed per day and has 100 pound of
feed in his farm.
a.
b.
c.
d.
Write a system of equations that describes the situation.
In how many days will Brad and Cliff have the same amount of feed left?
Does your answer to part b make sense?
How would your answer change if both Brad and Cliff receive a shipment of 100
pound of feed on day 4?
Name: ____________________________ Date: _________________Per:____
Student Page
Algebra/Day 2
Systems of Equations
Answer Page:
1 ANS: D
Let t represent the total amount paid and let d represent the number of days.
Nguyen’s Kennel:
Pup Palace:
Substitute
for t in the second equation and solve for w.
The costs for the two kennels are equal at 5 days. After that, the Pup Palace Kennel is cheaper.
A
B
C
D
Feedback
For a one day stay, the Pup Palace charges $47 while Nguyen's Kennel charges $35.
For a 10-day stay, Nguyen's Kennel charges $170 while the Pup Palace charges $155.
The Pup Palace becomes cheaper earlier than that. Set up cost equations for the two
kennels in terms of the number of days, and then set the equations equal and solve.
Correct!
2 ANS: A
Multiply all expressions in the second equation by
.
Add the two equations together.
Divide both sides by 2.
Solve for x.
Substitute the value for x into one of the original equations and
solve for y.
A
B
C
D
Feedback
Correct!
Multiply all terms in the second equation by -1 before combining the equations.
Multiply all terms in the second equation by -1 before combining the equations.
Multiply all terms in the second equation by -1 before combining the equations.
Name: ____________________________ Date: _________________Per:____
Student Page
Algebra/Day 2
Systems of Equations
3 ANS: D
The two-digit number can be represented as
the digit in the ones place.
, where x is the digit in the tens place and y is
The sum of the digits is 8.
4 times the number is 104.
Multiply the first equation by .
Distribute 4 in the second equation.
Add the two equations together.
Divide both sides by 36 to solve for x.
Choose the first equation to substitute.
Substitute 2 for x in the first equation.
Subtract 2 from both sides to solve for y.
The number is
A
B
C
D
.
Feedback
The second equation in the system involves the values of the digits.
The system of equations is correct. Now, use substitution to find the number.
The second equation in the system involves the values of the digits.
Correct!
4 a). Card A: C = 0.05m + 0.50
Card B C = 0.08m + 0.20
Set both cards equal to each other to solve for m.
b). 10 minutes
5 ANS: A
Let A be the admission fee and r be the rental fee. The equations would be 6A+5r=32 and
7A+5r=35.25. Subtract the first equation from the second equation to obtain A=3.25. Substitute in
3.25 for A in one of the equations and solve for r. 6(3.25)+5r=32, Simplify to obtain 19.5+5r+32,
subtract 19.5 from both sides, then divide both sides by 5 to obtain 2.5.
6 ANS: B
Let x be the amount of 67% solution, then 42-x would be the amount of 46% solution. The
equation would then be 0.67x+ 0.46(42-x) = 42(0.55). Use the distributive property to obtain
0.67 x + 19.32 − 0.46 x = 23.10 . Combine like terms, and subtract 19.32 from both sides, then
divide both sides by 0.21 to obtain 18L.
7 ANS: C
The first equation would be 3255+2.9d= cost, the second equation would be Revenue=13.75d.
The break even point occurs when cost and revenue are equal. Combine like terms by
subtracting 2.9d from both sides, then divide both sides by 10.85 to obtain 300, the number of
disks that need to be sold.
8 ANS: B
Name: ____________________________ Date: _________________Per:____
Student Page
Algebra/Day 2
Systems of Equations
9
⎧a = 70 − 12 f
⎩a = 100 − 15 f
a). ⎨
b). 10 days
c). No; they will both run out of food before that time.
d). the answer would make sense. Each farmer would have 50 lb of food on day 10.

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