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# Algebra/algebra 2

Question
1. Tickets for the homecoming dance cost \$25 for a single ticket or \$40 for a couple. Ticket sales totaled \$2930, and 142 people attended. How many tickets of each type were sold?

22 single; 120 couples  18 single; 62 couples
26 single; 57 couples  26 single; 114 couples

2. Two isosceles triangles have the same base length. The legs of one of the triangles is 3 times as long as the legs of the other. Find the lengths of the sides of the triangles if their perimeters are 22 cm and 50 cm.

6, 6, 10 for one triangle; 18, 18, 10 for the other  8, 8, 7 for one triangle; 24, 24, 2 for the other
7, 7, 9 for one triangle; 11.5, 11.5, 27 for the other  7, 7, 8 for one triangle; 21, 21, 8 for the other

3. A grain-storage warehouse has a total of 24 bins. Some hold 30 tons of grain each, and the rest hold 25 tons each. How many of each type of bin are there if the capacity of the warehouse is 640 tons?

14 30-ton bins; 10 25-ton bins  8 30-ton bins; 16 25-ton bins
2 30-ton bins; 22 25-ton bins  13 30-ton bins; 10 25-ton bins

4. With a head wind, a plane traveled 1200 miles in 4 hours. With the same wind as a tail wind, the return trip took 3 hours. Find the plane's air speed and the wind speed.

Air = 350 mph; Wind = 50 mph  Air = 325 mph; Wind = 25 mph
Air = 285 mph; Wind = 30 mph  Air = 370 mph; Wind = 30 mph

5. A caterer's total cost for catering a party includes a base cost, which is the same for every party. In addition the caterer charges a certain amount for each guest. If it costs \$350 to serve 20 guests and \$500 to serve 35 guests, find the base cost and the cost per guest.

\$100 base cost; \$12.50 per guest  \$150 base cost; \$10 per guest
\$150 base cost; \$15 per guest  \$100 base cost; \$12 per guest

6. For a recent job, a plumber earned \$32/hour, and the plumber's apprentice earned \$18/hour. The plumber worked 2 hours more than the apprentice. If together they were paid \$314, how much did each earn? (Hint: First write an expression for the number of hours each worked on the job.)

Plumber = \$256; Apprentice = \$58  Plumber = \$192; Apprentice = \$122
Plumber = \$242; Apprentice = \$72  Plumber = \$224; Apprentice = \$90

7. A plane whose air speed is 175 miles per hour flew from Monmouth to Laurens in 1.5 hours with a tail wind. On the return trip against the same wind, the plane was still 105 miles from Monmoth after 1.5 hours. Find the wind speed and the distance between Monmouth and Laurens.

Wind = 28 mph; Distance = 330 mi  Wind = 28 mph; Distance = 320 mi
Wind = 35 mph; Distance = 315 mi  Wind = 15 mph; Distance = 300 mi

8. While training for a biathlon race, Mike covered a total distance of 9 km by swimming for 45 minutes and running for 20 minutes. The next day he swam for 30 minutes and ran for 40 minutes, covering 14 km. Find his rates (in km/hr) for swimming and running. Assume these rates are constant.

Swims: 7 km/hour; Runs: 21 km/hr  Swims: 5 km/hr; Runs: 20 km/hr

9. In a certain mill the cost C in thousands of dollars of producing x tons of steel is given by C = 0.3x + 3.5. The revenue R in thousands of dollars from selling x tons is given by R = 0.5x. Find the point at which R = C (the break-even point).

17.5 tons  18 tons
16 tons  16.5 tons

10. Solve the system of functions.

3
x
x
+
-
2
y
y
=
=
4
-8

(0,4)  (0,2)
(1,-4)  (0,-4)

11. Martha's age is twice that of her brother Ned. The sum of their ages is 24. Find the age of each.

Martha: 12; Ned: 12  Martha: 8; Ned: 16
Martha: 16; Ned: 8  Martha: 21; Ned: 3

12. An apartment building contains 200 units. Some of these are one-bedroom units that rent for \$435 each month. The rest are two-bedroom units that rent for \$575 per month. When all of the units are rented, the total monthly income is \$97, 500. How many apartments are there of each type?

1br: 110; 2-br: 90  1-br: 150; 2-br: 50
1-br: 75; 2-br: 125  1-br: 125; 2-br: 75

13. The perimeter of a rectangle is 22 m. The length of the rectangle is 1 m less than 3 times the width. Find the length and the width.

length = 3 m; width = 8 m  length = 9 m; width = 2 m
length = 8 m; width = 3 m  length = 7 m; width = 4 m

14. Twice one number is 20 more than a second number. One-fourth of the first number is 2 less than 0.25 of the second. Find each number.

14, 34  28, 36
38, 52  10, 26

15. Solve the system of equations:

8
3
x
x
-
-
3
2
y
y
=
+
3
5

=

0

(3,7)  (3,-7)
(4,7)  (-3,-7)

16. Solve the system of equations:

5
3
x
x
+
-
6
2
y
y
+
+
8
16
=
=
0
0

(-6, 2)  (-4, 3)
(-4, 2)  (5,6)

17. Solve the system for (p,q):

3
9
p
p
+
-
2
1
q
q
=
=
-2
-6

( 1 , 0)

2

( -2 , 0)

3

( -2 , 2)

3

(0, -2 )

3

18. Solve the system:

3
5
x
x
-
+
2
3
y
y
=
+
6
9

=

0

(0,-3)  (1,3)
(0,-4)  (3,2)

19. Solve the system:

6
6
x
y
=
=
4
9
y
x
+
-
5
5

(10,0)  (0,10)
No solution  All real numbers

20. Solve the system for (c,d):

d
0.5
=
d
2
-
-
c
6
=
c
1

(-4,2)  (0,2)
(0,-4)  (2,0)

21. Solve the system:

x
x
+
-
y
y
=
=
4
2
(
(
y
y
+
+
2
4
)
)

Infinite solutions  (3,8)
No solution  (8,3)

22. Solve the system to find (u,v).  Hint:  x = 1/u and y = 1/v.  Use x and y in the equations to solve.  Once you solve for x and y, set those solutions equal to 1/u and 1/v, respectively, to find (u,v):

6 + 5 = 1
u v

3 - 10 = 3
u v

( 1 , -1 )
3
5

( 1 , -5)

5

(3,-5)  (-3,5)

23. Solve the system to find (u,v).  Hint:  x = 1/u and y = 1/v.  Use x and y in the equations to solve.  Once you solve for x and y, set those solutions equal to 1/u and 1/v, respectively, to find (u,v):

3 + 4 = 1
u v

6 - 2 = 1
u v

(5,10)
( 1 ,
1
)
5
10

( 1 ,
7
)
3
5

(10,5)

24. Megan has twice as many quarters as half-dollars. The total value is \$5.00. How many of each type of coin are there?

5 quarters; 10 half-dollars  10 quarters; 5 half-dollars
20 quarters; 2 half-dollars  2 quarters; 20 half-dollars

25. The cost of an adult ticket to a football game is \$2.00, and a student ticket is \$1.50. The total receipts from 300 tickets were \$550. How many tickets of each kind were sold?

26. A chemist has one solution containing 20% acid, and a second containing 30% acid. How many liters of each solution must be combined to obtain 80 liters of a mixture that is 28% acid?

70L of 20%, 10L of 30%  16L of 20%, 64L of 30%
15L of 20%, 65L of 30%  60L of 20%, 20L of 30%

27. A scientist wants to combine two metal alloys into 20 kg of a third alloy which is 60% aluminum. He plans to use one alloy with 45% aluminum content, and a second alloy with 70% aluminum content. How many kilograms of each alloy must be combined?

12 kg of 45%, 8 kg of 70%  10 kg of 45%, 10 kg of 70%
8 kg of 45%, 12 kg of 70%  9 kg of 45%, 11 kg of 70%

28. An \$8.50 assortment of pads contains \$0.65 pads and \$0.50 pads. If the number of \$0.50 pads is 1 less than half the number of \$0.65 pads, how many of each type of pad are in the assortment?

29. Flying with the wind, a plane can travel 1,500 miles in 2.5 hours. Flying at the same airspeed, the return trip against the wind requires 0.5 hour more to make the same trip. Find the airspeed.

150 mi/hr  250 mi/hr
350 mi/hr  550 mi/hr

30. The measure of the larger of two complementary angles is twice the measure of the smaller. Find the measure of each angle.

40, 80  30, 60
20, 40  50, 100

Part 2
Type the answer to the problem in the text box below each item. Be sure legibly show all work in your notebook. Remember to include any applicable units. If there is no solution, type "no solution". If there is not enough information present to solve the problem, type "not enough information". (Each question is worth one point)
31. The cost of an adult ticket to a football game is \$1.75. The cost of a student ticket is \$1.25. Total receipts last week from ticket sales were \$1,700. If the number of students tickets sold was twice the number of adult tickets, how many of each type were sold?

32. An airplane flies 840 mi in 3 hours with a tail wind. The return trip at the same airspeed takes 3.5 hours. Find the wind speed and the airspeed.

33. Solve the following system:

2x + y = -3

x + 3y = 1

34. Solve the following system:

3x - y = 4

x + 2y = -8

35. Solve the following system:

5x + 2y = 7

x - y = 7

1. 18 single, 62 couples
2. 7,7,8 for one; 21,21,8 for other
3. 8 30 ton, 16 25 ton
4. air = 350mph, wind = 50 mph
5. \$150 base, \$10 per guest
6. plumber \$224, helper \$90
7. wind = 35mph, distance = 315 miles
8. swim 4 km/hr, run 18 km/hr
9. 17.5 tons
11. martha 16, ned 8
12. 1 br 125, 2 br 75
13. length = 8, width = 3
14. 28,36
24. 10 quarters, 5 halves
26. 16L of 20%, 64L of 30%
27. 8 kg of 45%, 12 kg of 70%
29. 550mph
30. 30,60
32. Air 260mph, wind 20mph
33. x=-2, y=1
34. x=0, y=-4
35. x=3, y=-4

Algebra

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