Some problems that I would like help in (triangles, etc)

Paulinaaa

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Jun 21, 2006
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Hi I wanted to know if anyone can help me with these questions..I tried them but some of them I got wrong so I would like to review it with some of you.

1: A piece of paper 11 inches long is ripped into 3 pieces. The first piece is 3 inches more that twice the third piece. The second piece is 3 times the length of the third piece. What is the length of the second piece?

choices: 1 1/3 inches, 3 inches, 4 inches, 6 inches

10: A flag on a golf course is in the shape of a right triangle. The area of the flag is 156 square inch and its base is 12 inch, find the height of the flag.

choices: 12 inches, 13 inches, 22 inches, 26 inches

11: Angles A and B are complementary angles because their sum is 90 degrees. The measure of angle A is six degrees more than two times the measure of angle B. Find the measure of angle B.

choices: 42°, 30 °, 28°, 22°

14: A class is planning a trip to the Aquarium. They have saved $567 during the year for their annual field trip. Student tickets cost $12 and non-student tickets cost $15. If the number of students visiting the aquarium must be four times the number of non-student chaperones, how many students can visit the museum?

choices: 9, 25, 36, 40

15: Kim and Deb ride bicycles in opposite directions. Deb's speed is three miles per hour faster than Kim. If they are 16.5 miles apart in 1.5 hours, what is the speed of Kim?

choices: 4 mph, 5 mph, 7 mph, 9 mph
 
Paulinaaa said:
umm..I did the work..but Im not gonna do it all over again.
That may be why you have not done so well in class.
Mathematics is easy to learn. It just takes a lot of work.
If you do not want to work at it, you will not do well.
 
Paulinaaa said:
umm..I did the work..but Im not gonna do it all over again.
But you want the tutors to do it all over again...? :shock:

If you have done all the work, then you should have answers. What then is your question for us?

Thank you.

Eliz.
 
Hello Paulinaaa!

Paulinaaa said:
1: A piece of paper 11 inches long is ripped into 3 pieces. The first piece is 3 inches more that twice the third piece. The second piece is 3 times the length of the third piece. What is the length of the second piece?
Ok, our objective is to get an equation w/just one variable to solve. Ok?

So we can derive from the data:

\(\displaystyle x+y+z=11\) In which \(\displaystyle x\)=1st shred, \(\displaystyle y\)=the second shred, \(\displaystyle z\)=third shred.

The first piece is 3 inches more that twice the third piece= \(\displaystyle x=2z+3\)

The second piece is 3 times the length of the third piece= \(\displaystyle y=3z\)

So fill in our first equation for each with our other 2 equations:

\(\displaystyle x+y+z=11\)

\(\displaystyle (2z+3)+(3z)+(z)=11\)

Solve. Once you calculate \(\displaystyle z\), plug it in for the corresponding element in the equation to find your answer.

Paulinaaa said:
10: A flag on a golf course is in the shape of a right triangle. The area of the flag is 156 square inch and its base is 12 inch, find the height of the flag.
The area of a Triangle is \(\displaystyle \frac{bh}{2}\)
\(\displaystyle \frac{bh}{2}\)
\(\displaystyle \frac{12h}{2}=156\)
You can solve this.

Paulinaaa said:
11: Angles A and B are complementary angles because their sum is 90 degrees. The measure of angle A is six degrees more than two times the measure of angle B. Find the measure of angle B.
Once again you have another system of equations. :D

\(\displaystyle a+b=90\) (In which \(\displaystyle a\)=\(\displaystyle m\angle a, b=m\angle b\))

\(\displaystyle a=2b+6\)

So just fill in the \(\displaystyle a\) into your first equation and solve making:

\(\displaystyle 2b+6+b=90\)

Paulinaaa said:
14: A class is planning a trip to the Aquarium. They have saved $567 during the year for their annual field trip. Student tickets cost $12 and non-student tickets cost $15. If the number of students visiting the aquarium must be four times the number of non-student chaperones, how many students can visit the museum?
Another system of equations. 8-) Just remember whenever completeting these types of problems to always write out the equations you know cuz it will make it "click" on what to do.

So we can derive 2 equations once again:

\(\displaystyle 12s+14x=567\) In which \(\displaystyle s\) equals number of student tickets and \(\displaystyle x\) is equal to the number of non-student tickets.

\(\displaystyle s=4x\)

Now just plug in \(\displaystyle 4x\) into the \(\displaystyle s\) in our first equation since it is egalitarian to it, making the equation have one variable to solve, thus making an equation that is solvable.

Hence:

\(\displaystyle 12\(4x)+14x=567\)

Solve this equation and you have your answer.

Paulinaaa said:
15: Kim and Deb ride bicycles in opposite directions. Deb's speed is three miles per hour faster than Kim. If they are 16.5 miles apart in 1.5 hours, what is the speed of Kim?
Based on this info you can derive 2 systems of equations:

\(\displaystyle d=k+3\) (\(\displaystyle d\)=Deb's speed, \(\displaystyle k\)=Kim's speed)

Ok since \(\displaystyle distance=speed\bullet{time}\) you can conclude that:

Deb's \(\displaystyle distance=d\bullet\)1.5

Kim's \(\displaystyle distance=d-3\bullet{1.5}\)

Add these two equation together to get one "master" equation.

\(\displaystyle 1.5+1.5d-4.5=3d-4.5\)

Now how far apart the two? Right 16.5 miles.

So now you have two equations:

\(\displaystyle 3d-4.5=16.5\)
\(\displaystyle d=k+3\)

Solve the system and you have your master answer
 
You didn't have to do it all, Jonboy. Let's see what Paulinaaa can do. :wink:
 
happy said:
You didn't have to do it all, Jonboy. Let's see what Paulinaaa can do. :wink:

Yeah I may have overdone it but I kinda got bored but dont worry I dont do that everyday. I left the solving parts for Paulinaaa to do. She/He probably is already done with the problems and by the time Paulinaaa checks will already be done.
 
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