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 By: drstevewu (offline)  Monday, May 13 2013 @ 09:29 PM CDT (Read 1361 times)
drstevewu

Hi, I wonder if there is another solution to this question:

There were 544 brownies and cupcakes for sale at a bakery. All the brownies at the bakery cost \$448 more than all the cupcakes. After 4/5 of the brownies and 1/4 of the cupcakes were sold, there were twice as many brownies as cupcakes left. Each brownie cost \$0.80 less than each cupcake. How much did each brownie cost?

Thank you...

Junior

Registered: 04/20/10
Posts: 31

 By: echeewh (offline)  Tuesday, May 14 2013 @ 12:06 AM CDT
echeewh

Hi there,

Following pls find my worked solution:

<after>

B |------|------|
C |------|

<process>
B: (4/5) sold
C: (1/4) sold

<Work Backwards>

After (1/4)C was sold, its left with (3/4)C. So, split the 1 part (p) of C into 3. Likewise, the same with the 2 parts (p) of B.

Add 1p of C to its <before> model. Hence, ratio B : C is 6 : 4.

After (4/5)B was sold, its left with (1/5)B. So, split the 6p of B into 30 units (u), where 1p of B = 5u {common multiple of 6 and 5}. Likewise, the same with the 4p of C. giving it 20u.

(1/5)B = 30u
(5/5)B = 5 × 30 = 150u

Hence, ratio B : C is 150 : 20 = 15 : 2

<before>

B : C
15 : 2

Given a total of 544 B and C, we have ...

17u --> 544
1u --> 32

So ,
B = 15u --> 15 × 32 = 480
C = 2u --> 2 × 32 = 64

Given that each brownie cost \$0.80 less than each cupcake,

1B = 1C - 80

Given that all the brownies at the bakery cost \$448 more than all the cupcakes, Using <Number x Value> method> , we have ...

480 × (1C - 80) - 64C = 44800 {where 1C = cost of 1 cupcake}
480C - 38400 - 64C = 44800
416C = 44800 + 38400
416C = 83200
1C = 200 = \$2.00

Hence, 1B = 2.00 - 0.80 = \$1.20

========

Trust this helps.

Do let me know again if this is different from your <answerkey> or if theres further clarification.

Cheers,
Edward

Active Member

Registered: 04/21/11
Posts: 627

 By: PSRNatarajan (offline)  Tuesday, May 14 2013 @ 12:11 AM CDT
PSRNatarajan

Please see the attachment for the solution

Newbie

Registered: 03/26/12
Posts: 1

 By: drstevewu (offline)  Tuesday, May 14 2013 @ 10:39 AM CDT
drstevewu

Hey Edward, thank you very much again for your help..

PSRNatarajan, where can i view/find your attachment?

Junior

Registered: 04/20/10
Posts: 31

 By: xiaofenglim (offline)  Saturday, August 17 2013 @ 03:42 AM CDT
xiaofenglim

there are 10 red pens,2 green pens and 4 black pens in a box. what percentage of the pens in the box is black?

Newbie

Registered: 08/05/11
Posts: 1

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