MATHProblems 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?

vehicles $20

people $10

v

p

$ how many

20v

10p

total $

total t = 20v+10p

2. If r = 9, b = 5, and g = −6, what does (r + b − g)(b + g) equal?

14 6 5 6

20 1

20

9 5 6 5 6

r b g b g

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 made how many copies?

1st: 60

0 1 2 3 4 5 6 7 8

60

2nd:

60

80

60

80

60

80

60

80

60

80

60

80

480

480

960

Total

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 made how many copies?

60 copies 80 copies8 min 6 min

min min

480 copies 480 copies

960 copies

A Quicker Way (maybe)I like the first method many times because it helps me “get the feel

of the problem”.

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?

PinsGames1 - 5 1,200

Avg240

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?

PinsGames1 - 5 1,200

Avg240

6 3006-game

total1,500 250 250 6

?

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?

1200250

6

x

1500 1200 x

300 x

totalaverage

count

A Quicker Way (maybe)I like the first method many times because it helps me “get the feel

of the problem”.

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?

7.50

hours total$ amt

40 $300.00

2 $22.50 7.50 1.50

11.25

$322.50

regular

OT

42total

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?

7.50 8 11.25 2tot

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 11.25 400.00x

300 11.25 400x

11.25 100x

8.8 9x hrs

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

than theproduct of 10 and x

2x 3910x

7. If 9(x − 9) = −11, then x = ?

9 9 11x

9 81 11x

9 70x

81 81

9 9

70

9x

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:

$ / ticket tickets

$4.00

$6.50regular:

$60.00

$97.50

15

15

discount: $37.50

$97.50

15

9. The expression (3x − 4y2)(3x + 4y2) is equivalent to:

2 23 4 3 4x y x y

2 2 2 23 3 3 4 4 3 4 4x x x y y x y y

2 2 2 49 12 12 16x xy xy y

2 49 16x y

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?

A = 32

P = 24

6

6

66

6

8

24

24

6

4

length

widthP Area36

32

8

8

44

11. In ΔABC, the sum of the measures of ∠A and ∠B is 47°. What is the measure of ∠C ?

A

B

C

47°

C

47 180C

133C

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?

a

b

1

2

3

Item A2 choices

Item B3 choices

THEREFORE:When there are 2 and 3 choices,

there are 6 combinations.

a,1

a,2

a,3

b,1

b,2

b,3

Suppose you just had two items:

Item A has 2 choices (large or small)

Item B has 3 choices: (hats, coats, gloves)

I start EVERY "combination problem" with a simple example like this:

The General Rulemultiply the

number of objects in the sets.

3 sandwiches, 3 soups, 4 salads,

and 2 drinks

`

Combinations:

3 3 4 2

72

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 salad, and 1 drink?

a

b

1

2

3

A B

with 2 & 3 in a set, I get 6. Therefore,

I multiply ...

The problem has 3, 3, 2, and 4 items.

`

Combinations:

3 3 4 2

72

This happens very quick, once you get use to it!

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

18 19 57

smaller = s

bigger = b 3 × b

75

s + (3 × b)

19 20 60 79

Sometimes, it helps to start with the answers:

almost

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

3 1n n

3 1 79n n

3 3 79n n

4 3 79n

4 76n

19n

Suppose the two integers aren and n+1

smaller + (3 × bigger) =

Also, smaller +(3 × bigger) =

79

`

14. A function f(x) is defined as f(x) = −8x2. What is f(−3) ?

28f x x

8 9

72

23 8 3f

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

13 323 933 2743 81

3 4x

54