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 By: doreenJ (offline)  Monday, June 10 2013 @ 03:25 AM CDT (Read 3825 times)
doreenJ

Jodie has 20% more red beads than green beads. Her friend gave her 50 more orange beads than red beads. She mixed 20% of each of the colored beads to make a total of 22 bracelets. She had used 298 red and orange beads for all the bracelets . How many beads were there in each bracelet?

The answer for this question is 19 and I have no idea how to get it. :3

Newbie

Registered: 11/08/11
Posts: 3

 By: echeewh (offline)  Monday, June 10 2013 @ 04:29 AM CDT
echeewh

Hi Doreen,

Following pls find my worked solution:

R : G
120 : 100
6 : 5

O = 50 + 6p

Given that 298 red and orange beads were used for all the bracelets and 20% of each of the colored beads was used,

(1/5)R + (1/5)O = 298 beads
(6/5)p + 10 + (6/5)p = 298
(12/5)p = 298 - 10 = 288 beads
1p = 288 × (5/12) = 120 beads

(1/5)G = 1p = 120 beads

Given that 20% of each of the colored beads was used to make a total of 22 bracelets,

(1/5)R + (1/5)G + (1/5)O = 22 bracelets
298 + 120 beads = 22 bracelets
1 bracelet = 418 ÷ 22 = 19 beads

==========

Trust this helps.

Do let me know again if there's further clarification.

Cheers,
Edward

Active Member

Registered: 04/21/11
Posts: 627

 By: MathIzzzFun (offline)  Monday, June 10 2013 @ 10:18 AM CDT
MathIzzzFun

Quote by: echeewh

Hi Doreen,

Following pls find my worked solution:

R : G
120 : 100
6 : 5

O = 50 + 6p

Given that 298 red and orange beads were used for all the bracelets and 20% of each of the colored beads was used,

(1/5)R + (1/5)O = 298 beads
(6/5)p + 10 + (6/5)p = 298
(12/5)p = 298 - 10 = 288 beads
1p = 288 × (5/12) = 120 beads

(1/5)G = 1p = 120 beads

Given that 20% of each of the colored beads was used to make a total of 22 bracelets,

(1/5)R + (1/5)G + (1/5)O = 22 bracelets
298 + 120 beads = 22 bracelets
1 bracelet = 418 ÷ 22 = 19 beads

==========

Trust this helps.

Do let me know again if there's further clarification.

Cheers,
Edward

I would like to add that this is one of the many questions which are not set properly. While the total number of beads per bracelet is a whole number, the number of coloured beads in each bracelet may not be.
One can easily work out that 298 is not divisible by 22 which means that the total number of red and orange beads is not a whole number.

Number of beads per bracelet will be :
red --> 6 6/11
orange --> 7
green --> 5 5/11
which do not make sense unless we can cut beads to fractional portions.

cheers.

Chatty

Registered: 04/02/10
Posts: 36

 By: echeewh (offline)  Monday, June 10 2013 @ 05:46 PM CDT
echeewh

In fact , the number of each colored beads used need not be exactly the same for each bracelet. The color combination in each bracelet can be different and may vary from one bracelet to another. Afterall, its all about design and creativity. Hence, it does make sense and there's no need to cut the beads.

As I said previously, there are cases of questions not quite properly set. Yet, importantly it is essential for the child to learn and know how to solve the problem.

Thank you and best regards,
Edward

Active Member

Registered: 04/21/11
Posts: 627

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