Need help in forming equations for these two apparently simple scenarios!

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Mar 25th 2009, 04:39 AM
Rod

Need help in forming equations for these two apparently simple scenarios!

No. 1
Three eights of the class got sick. Three more students got sick, leaving only half the class at school. How many students were not sick?
(possible choice of answer: 8, 12, 16, 20)

No. 2
3/4 of a jar of lollies are multi-coloured and the rest are black. 6 of the black lollies are eaten and now there is 6/7 of the jar of multicoloured lollies. How many black lollies were in the jar at the start?
(possible answers: 6, 8, 10, 12)
Mar 25th 2009, 05:03 AM
masters

Quote:

Originally Posted by Rod

No. 1
Three eights of the class got sick. Three more students got sick, leaving only half the class at school. How many students were not sick?
(possible choice of answer: 8, 12, 16, 20)

No. 2
3/4 of a jar of lollies are multi-coloured and the rest are black. 6 of the black lollies are eaten and now there is 6/7 of the jar of multicoloured lollies. How many black lollies were in the jar at the start?
(possible answers: 6, 8, 10, 12)

Hi Rod,

1. Let x = the total number of students

$\frac{3}{8}x$ = the number who initially got sick

So, $\frac{3}{8}$ of the total + 3 more = $\frac{1}{2}$ the class (x).

Equation: $\frac{3}{8}x+3=\frac{1}{2}x$

Solve the equation to find the total number of students (x)

$x = 24$

$\frac{3}{8}\left(24\right)=9$ initially sick

$9+3=12$ total sick students

$24-12=12$ = number of students not sick.
Mar 25th 2009, 05:05 AM
stapel

Quote:

Originally Posted by Rod

No. 1: Three eights of the class got sick. Three more students got sick, leaving only half the class at school. How many students were not sick?

What is the difference between one-half and three-eighths? (Hint: Subtract.)

This fraction represents the three additional students. How many students were there, in total? (Hint: Since "1" means "one whole student body", figure out what you'd have to multiply by to convert the fraction from above into "1", and then multiply "3" by this value.)

What is half of this number? (Hint: Divide by 2.)

Quote:

Originally Posted by Rod

No. 2: 3/4 of a jar of lollies are multi-coloured and the rest are black. 6 of the black lollies are eaten and now there is 6/7 of the jar of multicoloured lollies. How many black lollies were in the jar at the start?

This one works very much like the last one:

If three-fourths were non-black, then one-fourth were black. If six-sevenths are now non-black, then one-seventh are now black.

What is the difference between one-fourth and one-seventh?

Since this fraction represents "six black", then what was the original number of black?

If you get stuck, please reply showing how far you have gotten. Thank you! :D
Mar 25th 2009, 05:15 AM
Rod

Many thanks!

Thanks for your help!
In the land of the blind, the one eyed man is king, but he still only has one eye!

Quote:

Originally Posted by masters

Hi Rod,

1. Let x = the total number of students

$\frac{3}{8}x$ = the number who initially got sick

So, $\frac{3}{8}$ of the total + 3 more = $\frac{1}{2}$ the class (x).

Equation: $\frac{3}{8}x+3=\frac{1}{2}x$

Solve the equation to find the total number of students (x)

$x = 24$

$\frac{3}{8}\left(24\right)=9$ initially sick

$9+3=12$ total sick students

$24-12=12$ = number of students not sick.
Mar 25th 2009, 05:34 AM
ADARSH

Quote:

Originally Posted by Rod

No. 1
Three eights of the class got sick. Three more students got sick, leaving only half the class at school. How many students were not sick?
(possible choice of answer: 8, 12, 16, 20)

No. 2
3/4 of a jar of lollies are multi-coloured and the rest are black. 6 of the black lollies are eaten and now there is 6/7 of the jar of multicoloured lollies. How many black lollies were in the jar at the start?
(possible answers: 6, 8, 10, 12)

Lets say there are x students in class
Initial case
No. of students who are sick = 3x/8

Second case
No. of students sick = x/2

According to question

3x/8 + 3 = x/2

---solve it
x = 24 , total no. of students healthy = x/2 = 12

-------------------------------------
Lets say initially x are there

Initial case
No. of colored = 3x/4
So no. of black = x/4

Second case
No. of black = x/4 - 6

No. of colored = 3x/4 (Unchanged)

But total no. this time = x-6

Hence Ratio is

$\frac{\frac{3x}{4}}{x-6} = \frac{6x}{7}$

----
$\frac{3}{4x-24} = \frac{6}{7}$

21 = 24x - 144

24x = 165

x= a fraction take this appx. value to the closest number , in other words do round-off

I hope I am not wrong (Thinking)
Mar 25th 2009, 06:04 AM
Rod

Can I rather solve by saying:
let x = number of coloured lollies and y = number of blacks

then the ratio 3/1 = x/y so x = 3y ........(1)

and y-6 = 6/7x ............................................ .(2)

substituting x = 3y in (2)

DOESN'T WORK!