Math 1 Assignment

I – Problem Solving

1.) Ten full crates of walnuts weight 410 pounds, whereas and empty crate weigh 10 pounds. How much do walnuts alone weigh?

Answer:

Let x – the weight of walnuts alone

10 Full crates of walnuts = 410 pounds

Crates alone = 10 pounds

Therefore

10 * (10+X) = 410

Divide both sides by 10 to get rid of 10 * (10+X) = 410 so the result would be 10+X=41

X would then mean 41-10 (Move 10 from left side of “=” sign to the right side and making it negative) so X = 41-10 = 31.

Walnuts alone weigh 31 pounds.

2.) If a family has 5 children, in how many ways could the parents have 2 boys and 3 girls are children?

Answer:

1 – boy

0 – girl

Ways to arrange

11000

10100

10010

10001

01100

00110

00011

01001

01010

Therefore there are 9 ways to arrange the children.

3.) Given two rows of the Pascal triangle, find the next row.

Answer:

Two rows of pascal triangle is

1

1 1

Next line would be

1

1 1

1 2(1+1) 1

II – Inductive and Deductive Reasoning

1.) Consider the ff. pattern : 9x1 – 1 =8

9x21-1 =188

9x321-1 =2888

9x4231-1 =38,888

Use this pattern and inductive reasoning to find the next problem and the next answer sequence:

Answer: The rows of the problems (9x1 – 1, 9x21-1, 9x321-1, 9x4231-1) shows that there is a counting sequence that spans from right to left. With this said, the next sequence would be starting from right to left of 1-5 (9X54321-1). On the answers part, the number of 8s would reflect on which part in the sequence it is (ex. 3rd part shows three 8s). The first number (8, 188, 2888, 38,888) would be the sequence number minus one (ex. 3rd part is 3-1 = 2). With those two points said, the answer would be the sequence number (5) minus one and five number of 8s = 488888. The whole problem and answer would then be 9 X 54321 – 1 =488,888.

2.) Find the 6 pattern.

Answer: Given the explanation above, the answer would be 9 X 654321 – 1 =5,888,888

III - Problem solving with sets

1.) From a survey of 100 college students, a marketing research company found that 75 students own stereos, 45 own cars, and 35 owned both a car and a stereo.

a.) How many students owned either a car or a stereo but not both?

Answer:

The Diagram Below shows the Relationship

X are the number of students owning a stereo only

Y is the number of students owning a car only

X would then be 75 – 35 = 40

Y would then be 45 – 35 = 10

Therefore there are 40+10 = 50 students that own a car and a stereo but not both.

b.) How many students didn’t own a car or a stereo?

Answer

As gotten above there are 40 students that own a stereo only, 10 students which own a car only and 35 students which own both. Adding these numbers (40+10+35=85) would yield 85 students that one/both of a car or stereo. The total number of students is 100, subtracting 85 from 100 would yield 15 students that own nothing.

2.) Let U = {1,2,3,4,5,6,7}, A{1,2,3,4}, B{1,2,5,6} C{3,5,7}

List the elements of each set:

1.) AUB 2.) A∩B 3.) A U (B∩C) 4.) A-B 5.) B-C

Answer:

1.) A union B is A combined with B. AUB = {1,2,3,4,5,6}

2.) A intersection B shows the set which contains the elements that exist in both A and B. A∩B={1,2}

3.) A U (B∩C). First get B∩C which is {5}. Combine this with a to get A U (B∩C) = {1,2,3,4,5}.

4.) A minus B shows the elements of A removed with elements that are present in B. A-B is then {3,4}

5.) B-C would then be {1,2,6}.

3.) Draw a Venn diagram showing the relationship among cats, dogs and animals.

IV. Logic