### Math Problems

```MATH
Problems 1-15
I’ll have more problems up this weekend.
1. The weekly fee for staying at the
Pleasant Lake Campground is \$20 per
vehicle and \$10 per person. Last year,
weekly fees were paid for v vehicles and p
persons. Which of the following expressions
gives the total amount, in dollars, collected
for weekly fees last year?
\$
how many
total \$
vehicles
\$20
v
20v
people
\$10
p
10p
total
t = 20v+10p
2. If r = 9, b = 5, and g = −6, what does
(r + b − g)(b + g) equal?
 r  b  g b  g 
  9  5   6    5   6  
 14  6  5  6 
  20  1
 20
3. A copy machine makes 60 copies per
minute. A second copy machine makes 80
copies per minute. The second machine
starts making copies 2 minutes after the
first machine starts. Both machines stop
making copies 8 minutes after the first
machine started. Together, the 2 machines
0
1st:
2nd:
1
60
3
2
60
4
6
5
7
8
60
60
60
60
60
60
Total
480
80
80
80
80
80
80
480
960
3b. A copy machine makes 60 copies per
minute. A second copy machine makes 80
copies per minute. The second machine
starts making copies 2 minutes after the
first machine starts. Both machines stop
making copies 8 minutes after the first
machine started. Together, the 2 machines
A Quicker Way (maybe)
I like the first method many times
because it helps me “get the feel
of the problem”.
 60 copies 
 80 copies 
8
min






  6 min 
 min 
 min 
 480 copies  480 copies
 960 copies
4. Marlon is bowling in a tournament and
has the highest average after 5 games, with
scores of 210, 225, 254, 231, and 280. In
order to maintain this exact average, what
must be Marlon’s score for his 6th game?
Games
1-5
Pins
1,200
Avg
240
4b. Marlon is bowling in a tournament and
has the highest average after 5 games, with
scores of 210, 225, 254, 231, and 280. In
order to average 250, what must Marlon
score on his last game?
Games
1-5
6
6-game
total
Pins
1,200
?
300
1,500
 250  6
Avg
240
250
4b. Marlon is bowling in a tournament and
has the highest average after 5 games, with
scores of 210, 225, 254, 231, and 280. In
order to average 250, what must Marlon
score on his last game?
A Quicker Way (maybe)
I like the first method many times
because it helps me “get the feel
of the problem”.
average 
250 
total
count
1200  x
6
1500  1200  x
300  x
5. Joelle earns her regular pay of \$7.50 per
hour for up to 40 hours of work in a week.
For each hour over 40 hours of work in a
week, Joelle is paid 1½ times her regular
pay. How much does Joelle earn for a week
in which she works 42 hours?
regular
OT
\$ amt
hours
total
7.50
40
\$300.00
2
\$22.50
42
\$322.50
 7.501.50
 11.25
total
5b. Joelle earns her regular pay of \$7.50
per hour for up to 40 hours of work in a
week. For each hour over 40 hours of work
in a week, Joelle is paid 1½ times her
regular pay. How much does Joelle earn
for a week in which she works 42 hours?
tot   7.508  11.25 2 
 300.00  22.50
 322.50
5c. Joelle earns her regular pay of \$7.50
per hour for up to 40 hours of work in a
week. For each hour over 40 hours of work
in a week, Joelle is paid 1½ times her
regular pay. She owes her Dad \$400. If she
works 40 hours during the week, how long
does she have to work on Saturday to repay
her Dad? (assume she must work complete
hours).
 40 7.50   x 11.25  400.00
300  11.25x  400
11.25x  100
x  8.8  9hrs
6. Which of the following mathematical
expressions is equivalent to the verbal
expression “A number, x, squared is 39
more than the product of 10 and x” ?
a number,
x, squared
is
39 more product of
than the 10 and x
x  39 10x
2
7. If 9(x − 9) = −11, then x = ?
9  x  9   11
9 x  81  11
81 81
9 x  70
9
9
x
70
9
8. Discount tickets to a basketball
tournament sell for \$4.00 each. Enrico
spent \$60.00 on discount tickets, \$37.50 less
than if he had bought the tickets at the
regular price. What was the regular ticket
price?
paid:
\$60.00
discount:
\$37.50
regular:
\$97.50
\$ / ticket
tickets
\$4.00
15
\$6.50
\$97.50

15
15
9. The expression (3x − 4y2)(3x + 4y2) is
equivalent to:
3x  4 y 3x  4 y 
  3x  3x    3x   4 y    4 y   3x    4 y  4 y 
2
2
2
 9 x2  12 xy 2  12 xy 2  16 y 4
 9 x2  16 y 4
2
2
2
10. A rectangle has an area of 32 square
feet and a perimeter of 24 feet. What is the
shortest of the side lengths, in feet, of the
rectangle?
6 8
A = 32
P = 24
6
4
6
4
6 8
P
24
length
6
24
8
width
6
4
Area
36
32
11. In ΔABC, the sum of the measures of
∠A and ∠B is 47°. What is the measure of
∠C ?
B
C  47  180
C  133
A
C
C
12. In the school cafeteria, students choose
their lunch from 3 sandwiches, 3 soups, 4
salads, and 2 drinks. How many different
lunches are possible for a student who
chooses exactly 1 sandwich, 1 soup, 1 salad,
and 1 drink?
I start EVERY "combination problem"
with a simple example like this:
Suppose you just had two items:
Item A has 2 choices (large or small)
Item B has 3 choices: (hats, coats, gloves)
The General Rule
multiply the
number of objects
in the sets.
3 sandwiches, 3
and 2 drinks
Item A
2 choices
a
b
Item B
3 choices
a,1 b,1
1
2
a,2 b,2
3
a,3 b,3
`
Combinations:
 3 3 4  2
 72
THEREFORE:
When there are 2 and 3 choices,
there are 6 combinations.
12b. In the school cafeteria, students
choose their lunch from 3 sandwiches, 3
soups, 4 salads, and 2 drinks. How many
different lunches are possible for a student
who chooses exactly 1 sandwich, 1 soup, 1
This happens very quick, once you get
use to it!
A
B
a
1
b
2
3
The problem has 3,
3, 2, and 4 items.
with 2 & 3 in a set,
I get 6. Therefore,
I multiply ...
`
Combinations:
 3 3 4  2
 72
13. For 2 consecutive integers, the result of
adding the smaller integer and triple the
larger integer is 79. What are the 2
integers?
A. 18, 19
B. 19, 20
C. 20, 21
D. 26, 27
Sometimes, it helps to start
E. 39, 40
with
smaller
=s
bigger
=b
3×b
s + (3 × b)
18
19
57
75
almost
19
20
60
79
yes
13. For 2 consecutive integers, the result of
adding the smaller integer and triple the
larger integer is 79. What are the 2
integers?
A. 18, 19
B. 19, 20
C. 20, 21
D. 26, 27
E. 39, 40
Suppose the two
integers are
n and n+1
Also, smaller +
(3 × bigger) =
79
smaller +
(3 × bigger) =
n  3 n  1
`
n  3 n  1  79
n  3n  3  79
4n  3  79
4n  76
n  19
14. A function f(x) is defined as f(x) = −8x2.
What is f(−3) ?
f  x   8x 2
f  3  8  3
 8  9 
 72
2
15. If 3x = 54, then which of the following
must be true?
A. 1 < x < 2
B. 2 < x < 3
C. 3 < x < 4
D. 4 < x < 5
E. 5 < x
31  3
32  9
33  27
3  81
4
3 x  4
54
```