HOMEWORK HELP! MATH 208 WORD PROBLEMS

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Instructions
Attempt all questions. Answers must be justified in order to gain full credit.

1. A watermain for a street is being laid using a particular kind of pipe that comes in either 18-foot sections
or 20-foot sections. The designer has determined that the water main would require 14 fewer sections of
20-foot pipe than if 18-foot sections were used. Find the total length of the water main.

2. Two friends are shopping together when they encounter a special “3 for 2” show sale. If they purchase
two pairs of shoes at the regular price, a third pair (of lower or equal value) will be free. Neither friend
wants three pairs of shoes, but pat would like to buy a $56 and a $39 pair while Chris is interested in a
$45 pair. If they buy the shoes together to take advantage of the sale, what is the fairest share for each to
pay?

3. Convert the base two numeral 10101010two into a base eight numeral.

4. Let R be the relation on A = {1, 2, 3, 4} defined by
R = {(1, 2), (2, 3), (1, 4), (2, 4), (4, 2), (2, 1), (4, 1), (3, 2)}
Is R reflexive? Symmetric? Transitive? An equivalence relation?

5. Find the 47th term and the nth term of the following sequence.
3, 7, 11, 15, 19, · · ·

6. Write down your favorite three-digit number twice to form a six-digit number (e.g. 587,587). Is your
six-digit number divisible by 7? How about 11? How about 13? Does this always work? Why? (Hint:
Expanded form.)


please help with any problem any help is good thank you very much

 

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second part:

7. A pad of 200 sheets of paper is approximately 15 mm thick. Suppose that one piece of this paper were
folded in half, then folded in half again, then folded again, and so on. If this folding process was continued
until the piece of paper had been folded in half 30 times, how thick would the folded paper be?

8. Use the lattice method to compute the sum 1T 8eleven + 499eleven.
11. Use the scaffold method of division to compute 2134six ÷ 14six. (Hint: Write out the base six multiplication
table to help you out.)

9. Betty has three times as much money as her brother Tom. If each of them spends $1.50 to see a movie,
Betty will have nine times as much money left over as Tom. How much money does each have before
going to the movie?

Thanks for any help that is given I am currently working on this and I need as much help as possible this assignment will determine if I pass or fail

 

[Denis]

Did you read "Read before posting" ?

 

[stapel]

I need as much help as possible this assignment will determine if I pass or fail

Actually, if you are to pass the course, then I'm afraid you will need to participate in it. :shock:

Please reply with a clear listing of your work and reasoning so far. Thank you!

Eliz.

 

[soroban]

Hello, infil!

Here's some help . . .

3. Convert the base two numeral \(\displaystyle 10101010_2\) into a base-eight numeral.

We could covert it to base-ten, then to base-8.
But there is a "trick" for this particular problem.

\(\displaystyle \text{Divide the number into groups-of-three, starting at the right: }\:|010|101|010|\)

\(\displaystyle \text{Convert each 3-digit group to base-eight: }\;|\underbrace{010}_2|\underbrace{101}_5|\underbrace{010}_2|\)

\(\displaystyle \text{Therefore: }\;10101010_2 \;=\;252_8\)

5. Find the 47th term and the nth term of this sequence: 3, 7, 11, 15, 19, . . .

This is an arithmetic sequence with first term \(\displaystyle a = 3\) and common difference \(\displaystyle d = 4.\)

\(\displaystyle \text{The }n^{th}\text{ term is: }\:a_n \:=\:a + (n-1)d \quad\Rightarrow\quad a_n \:=\:3 + (n-1)4\)

\(\displaystyle \text{The }47^{th}\text{ term is: }\:a_{47} \;=\;3 + (46)(4) \;=\;187\)

6. Write down your favorite three-digit number twice to form a six-digit number (e.g. 587,587).
Is your six-digit number divisible by 7? .By 11? .By 13?
Does this always work? . Why?

\(\displaystyle \text{A number of the form: }\,N \:=\:abcabc\,\text{ is actually: }\:1001 \times abc\)

\(\displaystyle \text{Since }\,1001 \;=\;7 \times 11 \times 13\text{, then }\,N \;=\;7\cdot11\cdot13\cdot abc\)

. . \(\displaystyle \text{Therefore, }N\text{ is always divisible by 7, 11 and 13.}\)

 

[soroban]

Hello again, infil!

7. A pad of 200 sheets of paper is approximately 15 mm thick.
Suppose that one piece of this paper were folded in half, then folded in half again,
then folded again, and so on.
If this folding process was continued until the piece of paper had been folded in half 30 times,
how thick would the folded paper be?

\(\displaystyle \text{One sheet is: }\:\frac{15\text{ mm}}{200} \:=\:0.075\text{ mm thick.}\)

\(\displaystyle \text{After 30 foldings, the paper would be: }\:2^{30} \:=\:1,\!073,\!741,\!824\text{ sheets thick.}\)

\(\displaystyle \text{It would be: }\:1,\!073,\!741,\!824 \times 0.075 \:=\:80,\1530,\!636.8\text{ mm} \;= \;80,\!530.6\text{ meters}\)

. . . . . . . . \(\displaystyle = \;80.5\text{ km} \;\approx\;50\text{ miles thick.}\)

\(\displaystyle \text{8. Use the lattice method to compute the sum: }\:1T8_{11} + 499_{11}\)

I am not familiar with the "lattice method", but it looks like this:


. . \(\displaystyle \begin{array}{cccc} & 1 & T & 8 \\ + & 4 & 9 & 9 \\ --&--&--&-- \\ & 6 & 9 & 6 \end{array}\)

\(\displaystyle \text{11. Use the scaffold method of division to compute: }\:2134_6 \div 14_6\)

I'm not familiar with the "scaffold method" either . . .


. . \(\displaystyle \begin{array}{cccccc} & & & 1 & 2 & 1 \\ & & -- & -- & -- & -- \\ 1\quad4 & ) & 2 & 1 & 3 & 4 \\ & & 1 & 4 \\ & & -- & -- \\ & & & 3 & 3 \\ & & & 3 & 2 \\ & & & -- & -- \\ & & & & 1 & 4 \\ & & & & 1 & 4 \\ & & & & -- & -- \end{array}\)