Problem Solving

[phoenix9801]

Please I need help clarification- For understanding purpose, can you explain in details.

Problem 3:

____l_____l__________l___ L
....A.....B.................C

On line L, the length of BC is 1.5 times the length of AB. If the length of AC is 30, what is the length of AC is 30, What is the Length of BC?


A) 10
B) 12
C) 15
D) 18
E) 20

Can you how to solve the problem algebra for example [ BC =1.5 (AB)]?



__________

Problem 4:

Four containers of flour are on the table: the first contains 1/3 of pound, the second contains 1/6 of a pound, the third contains 1/9 of a pound, and the fourth contains 1/18 of a pound. If each container can hold one pound of flour, how many additional pounds of flour are required to fill all four containers ?

A) 2/9
B) 2/3
c) 11/9
D) 25/9
E) 10/3

How can you answer the question using Boll Parking or Estimating???

[aneesh.kg]

First problem:
AC = AB + BC
Given: AC = 30
So
30 = AB + BC -- (1)
Also Given: BC = (3/2)*AB
So
AB = (2/3)*BC -- (2)

Substituting AB in Equation (1):
30 = (2/3)*BC + BC
30 = BC*(1 + 2/3)
BC = 30*(3/5)
BC = 18

[spoiler](D)[/spoiler] is the answer

[aneesh.kg]

Why do you want to estimate or make ball park guesses when this is easy to calculate? Is there a particular reason?

Second problem:

To calculate how much we need to fill in each container, we need to subtract the weight of the flour in it from its capacity (1 pound).

So, you have to fill
(1 - 1/3) + (1 - 1/6) + (1 - 1/9) + (1 - 1/18) pounds
= 2/3 + 5/6 + 8/9 + 17/18 pounds
Taking 18 at the denominator,
(12 + 15 + 16 + 17)/18
= 60/18
= [spoiler]10/3[/spoiler]

[spoiler](E)[/spoiler] is the answer.

[phoenix9801]

two questions how did you get 2/3 from please explain and how did you move from 30 = BC*(1 + 2/3) to
BC = 30*(3/5)? I thought it was going to be -30*(3/5)? Thanks

First problem:
AC = AB + BC
Given: AC = 30
So
30 = AB + BC -- (1)
Also Given: BC = (3/2)*AB
So
AB = (2/3)*BC -- (2)

Substituting AB in Equation (1):
30 = (2/3)*BC + BC
30 = BC*(1 + 2/3)
BC = 30*(3/5)
BC = 18

[spoiler](D)[/spoiler] is the answer

[phoenix9801]

Thanks, But I solved the same you did also and I know it is much easier, But I would like to know also how to to estimate or make ball park guesses Please? please explain in detail I would greatly appreciate it.

Why do you want to estimate or make ball park guesses when this is easy to calculate? Is there a particular reason?

Second problem:

To calculate how much we need to fill in each container, we need to subtract the weight of the flour in it from its capacity (1 pound).

So, you have to fill
(1 - 1/3) + (1 - 1/6) + (1 - 1/9) + (1 - 1/18) pounds
= 2/3 + 5/6 + 8/9 + 17/18 pounds
Taking 18 at the denominator,
(12 + 15 + 16 + 17)/18
= 60/18
= [spoiler]10/3[/spoiler]

[spoiler](E)[/spoiler] is the answer.

[aneesh.kg]

Doubt (1):
BC = (2/3)*AB
Multiplying both sides by 3/2,
(3/2)*BC = AB

Doubt (2):
30 = BC*(1 + 2/3)
On the Right Hand Side alone,
30 = BC*(3/3 + 2/3)
30 = BC*(5/3)

Well, as far as the estimation is concerned, you can see that all the containers contain very less flour. So, we have to fill a major volume of each container with flour. The total volume of the four containers is 4, so the answer a little smaller than 4 should be the answer.
Only 10/3 meets that criteria. 25/9 is much farther from 4. All the other options are easily ruled out.

But, I will not advise this method because there could have been two very close options. Please don't look for guesses and estimations.

[phoenix9801]

I do not mean to pain in the neck. forgave me, so how would you do it in term of 1.5 and multiply both sides by the inverse without using fractions.

Doubt (1):
BC = (2/3)*AB
Multiplying both sides by 3/2,
(3/2)*BC = AB

Doubt (2):
30 = BC*(1 + 2/3)
On the Right Hand Side alone,
30 = BC*(3/3 + 2/3)
30 = BC*(5/3)

Well, as far as the estimation is concerned, you can see that all the containers contain very less flour. So, we have to fill a major volume of each container with flour. The total volume of the four containers is 4, so the answer a little smaller than 4 should be the answer.
Only 10/3 meets that criteria. 25/9 is much farther from 4. All the other options are easily ruled out.

But, I will not advise this method because there could have been two very close options. Please don't look for guesses and estimations.

[aneesh.kg]

Oh I am happy that you are getting your doubts clarified.

You can solve it using 1.5 also.
BC = 1.5*AB
Dividing both sides by 1.5,
(1/1.5)*BC = AB
and (1/1.5 = 0.666.., and by 0.666.., I mean 0.6 recurring)
(0.666..)*BC = AB
0.666.. = 2/3
So
(2/3)*BC = AB

But, hey, Fractions are much easier to work with than Decimals. Don't you think so?

Is it clear now? Let me know if it is not.

[phoenix9801]

your properly hate me by now. LOL . I do understand some what by now.
The question is now if I continue using decimals to get the same answer compare to fraction how would I do that?

Fraction.........VS.....Decimals
30=BC *(1+2/3) ........30=BC*(1+.6666) ?????
BC= 30*(3/5)
BC=18

Note: Since adding 1+2/3 is not the same as 1+.666)????

Oh I am happy that you are getting your doubts clarified.

You can solve it using 1.5 also.
BC = 1.5*AB
Dividing both sides by 1.5,
(1/1.5)*BC = AB
and (1/1.5 = 0.666.., and by 0.666.., I mean 0.6 recurring)
(0.666..)*BC = AB
0.666.. = 2/3
So
(2/3)*BC = AB

But, hey, Fractions are much easier to work with than Decimals. Don't you think so?

Is it clear now? Let me know if it is not.

[aneesh.kg]

(1 + 2/3) is exactly equal to (1 + 0.666 recurring)

30 = BC*(1 + 0.666)
30 = 1.666*BC
BC = 30/1.666.. = 18
But you might need a calculator to get the answer.

However, the fractions are easily solvable.
1.666.. = 1 + 0.666.. = 1 + 2/3 = 5/3
So
BC = 30/((5/3) = 30*3/5 = 18

[gmacpup]

Ans to Q1
Say AB=x
BC=1.5 times AB = 1.5x

AB+ BC = AC
i.e. x+1.5x=30 (given)
2.5x=30
x=12=AB

Hence, BC=1.5(12)=18

[gmacpup]

Why do you want to estimate or make ball park guesses when this is easy to calculate? Is there a particular reason?

Second problem:

To calculate how much we need to fill in each container, we need to subtract the weight of the flour in it from its capacity (1 pound).

So, you have to fill
(1 - 1/3) + (1 - 1/6) + (1 - 1/9) + (1 - 1/18) pounds
= 2/3 + 5/6 + 8/9 + 17/18 pounds
Taking 18 at the denominator,
(12 + 15 + 16 + 17)/18
= 60/18
= [spoiler]10/3[/spoiler]

[spoiler](E)[/spoiler] is the answer.

I got the same answer too! (E)