Math 125
EXAM #2
Name:_______________________________________________
Complete all problems in your blue book.
Copy the problem into the bluebook then show all of the required work for that problem.
Work problems out down the page, not across.
Make only one column of work per page.
Skip a line between each problem.
Any work or answers completed on this test form, other than the problems that require you to graph, will not be graded.
For problems that REQUIRE YOU TO GRAPH use the graphs provided on this test form and complete the work for
those problems in the space next to the graph. If you feel that you need more room, then indicate next to the graph that
the work is in your bluebook.
Complete, organized, and correct work, using the methods taught in class and including correct use of symbols, is required
to receive full credit. Partial or no credit will be given when work is missing. Each problem is worth 5 points.
SHOW ALL WORK . DO NOT ROUND ANSWERS UNLESS INSTRUCTED TO DO SO. Express answers in lowest
terms. Simplify all radicals.
Solve the equation.
5
1
1
( y - 3)
1) y - (y + ) =
9
2
72
72
5
1
1
y - (y + ) =
( y - 3)72
9
2
72
40y - 72(y +
1
)=y-3
2
40y - 72y - 36 = y - 3
-32y - 36 = y - 3
-36 = 33y - 3
-33 = 33y
-1 = y
2)
(8x + 2) (10x - 3)
=
5
12
12(8x + 2) = (10x - 3)5
96x + 24 = 50x - 15
46x + 24 = -15
46x = -39
39
x=46
3) 7(x + 8) -16x = -9(x + 5) + 16
7x + 56 - 16x = -9x - 45 + 16
56 - 9x = -9x - 29
56 = -29
4) 3(9x + 4) - 21x = 3(2x + 6) - 23
27x + 12 - 21x = 6x + 18 - 23
6x + 12 = 6x - 5
1
5) 0.04(50) + 0.4x = 0.2(50 + x)
2 + .4x = 10 + .2x
2 + .2x = 10
.2x = 8
x = 40
6)
1
4
17
=
15
x
1
x = 15(17)
4
4
1
x = 15(17)(4)
4
x = 1025
Set-up an equation and use it to solve the problem.
7) The difference between two positive integers is 32. One integer is three times as great as the other. Find the
integers.
x - y = 32
3y - y = 32
2y = 32
y = 16
x = 3y
x = 3(16)
x = 48
The integers are 16 and 48
8) If 5 is added to a number and the sum is tripled, the result is 27 more than the number. Find the number.
3(x + 5) = x + 27
3x + 15 = x + 27
2x + 15 = 27
2x = 12
x=6
9) Jessica has a rope that is 22 feet long. She cuts the rope into three pieces so that the largest piece is seven less
than twice the middle piece and the middle piece is three more than the smallest piece. How big is the middle
piece?
s + (s + 3) + (2m - 7) = 22
s + (s + 3) + [2(s + 3) - 7] = 22
2s + 3 + [2s + 6 - 7] = 22
4s + 2 = 22
4s = 20
s=5
m=5+3
m=8
middle piece is 8 feet long
2
s: small piece
m: middle piece = s + 3
10) On August 1, the Davidson family received 23 pieces of mail, consisting of magazines, bills, letters, and ads. If
they received the same number of magazines as letters, three more bills than letters, and five more ads than
bills, how many magazines did they receive?
M + B + L + A = 23
M + (M + 3) + M + (B + 5) = 23
M + (M + 3) + M + (M + 3 + 5) = 23
4M + 11 = 23
4M = 12
M=3
M: # of magazines
B = # of bills
L: # of letters = M
A: # of ads
3 magazines
11) If three times the smaller of two consecutive integers is added to four times the larger, the result is 46. Find the
smaller integer.
4 x + 1 + 3x = 46
4x + 4 + 3x = 46
7x + 4 = 46
7x = 42
x=6
12) Find the measure of an angle such that the difference between its supplement and 3 times its complement is
48°.
180 - x - 3 90 - x = 48
18 - x - 270 + 3x = 48
2x - 90 = 48
2x = 138
x = 69
13) A square plywood platform has a perimeter which is 9 times the length of a side, decreased by 20. Find the
length of a side.
4x = 9x - 20
-5x = -20
x=4
14) The sum of three consecutive odd integers is 249. Find the integers.
x + x + 2 + x + 4 = 249
3x + 6 = 249
3x = 243
x = 81
81 + 2 = 83
3
81 + 4 = 85
15) A pharmacist found at the end of the day she had
5
as many prescriptions for antibiotics as tranquilizers. She
3
had 64 prescriptions altogether. How many did she have for antibiotics?
A=
5
T
3
A + T = 64
5
T + T = 64
3
3
5
T + T = 64(3)
3
A: # of antibiotics
A=
T: # of tranquilizers
5
(24)
3
A = 40
5t + 3T = 192
8t = 192
T = 24
16) A merchant has coffee worth $30 a pound that she wishes to mix with 80 pounds of coffee worth $80 a pound
to get a mixture that can be sold for $70 a pound. How many pounds of the $30 coffee should be used?
30x + 80(80) = 70(x + 80)
30x + 6400 = 70x + 5600
6400 = 40x + 5600
800 = 40x
20 = x
17) A chemist has two solutions of HCL. One has a 40% concentration and the other has a 25% concentration.
How many liters of each must be mixed to obtain 98 liters of a 34% solution?
.40x + .25y = .34(98)
.40(98 - y) + .25y = 33.32
39.2 - .40y + .25y = 33.32
-.15y = -5.88
y = 39.2
x + y = 98
x = 98 - y
x = 98 - 39.2
x = 58.8
18) A woman has $1.70 in dimes and nickels. She has 2 more dimes than nickels. How many nickels does she
have?
.10d + .05n = 1.70
.10(n + 2) + .05n = 1.70
.10n + .20 + .05n = 1.70
.15n + .20 = 1.70
.15n = 1.50
n = 100
d: # of dimes = n + 2
n: # of nickels
19) Roberto invested some money at 7%, and then invested $5000 more than twice this amount at 12%. His total
annual income from the two investments was $4940. How much was invested at 12%?
.07x + .12(2x + 5000) = 4940
.07x + .24x + 600 = 4940
.31x + 600 = 4940
.31x = 4340
x = 14000
4
2(14000) + 5000
28000 + 5000
$33,000 @ 12%
20) A truck enters a highway driving 60mph. A car enters the same highway at the same place 10 minutes later
and drives 72mph in the same direcrtion. How long will it take the car to pass the truck?
60 t +
10
= 72t
60
60t + 10 = 72t
10 = 12t
10
=t
12
5
=t
6
21) Two sides of a triangle have the same length. the third side measures 6m less than twice the common length.
The perimeter of the triangle is 10m. What are the lengths of the three sides?
x + x + (2x - 6) = 10
4x - 6 = 10
4x = 16
x=4
2(4) - 6
8-6
2
the sides measure 4m, 4m, 2m
Use a proportion to solve the problem.
22) On a map of the Thunderbird Country Club golf course, 2.5 inches equals 60 yards. How long is the 6th hole if
the map shows 16 inches?
2.5in
16in
=
60yd
x
2.5x = 60(16)
960
x=
2.5
x = 384yd
Find the measure of each marked angle.
23)
(11x + 2)°
(14x + 3)°
(11x + 2) + 14x + 3 = 180
25x + 5 = 180
25x = 175
x=7
5
11(7) + 2
77 + 2
79
180 - 79
101
Solve the formula for the specified variable.
9
24) F = C + 32 for C
5
F - 32 =
9
C
5
5
9 5
F - 32 = C
9
5 9
5
F - 32 = C
9
Find the unit price for each item to the nearest cent. Tell which brand is the better buy.
25) Brand A 32 oz for $8.64 Brand B 28 oz for $7.00
Brand A
$8.64
32oz
Brand B
$7.00
28oz
$.27/oz
$.25/oz
Brand B is the better buy
CHOOSE ONLY ONE BONUS QUESTION TO DO. (10 points)
Solve the problem.
26) A reservation clerk worked 9 hours one day. She spent twice as much time entering new reservations as she
did verifying old ones and one and a half as much time calling to confirm reservations as verifying old ones.
How much time did she spend entering new reservations?
27) It is necessary to have a 40% antifreeze solution in the radiator of a certain car. The radiator now has 30 liters of
20% solution. How many liters of this should be drained and replaced with 100% antifreeze to get the desired
strength?
6