word transl - qbank # 22 - lighter luggage

[sanjivsp]

below is the problem and the answer explanation. my answer would have 12 pounds. ie there was 32 pounds of bks, 20 of clothing, 12 elec. he took out 4 lbs of clothing which doubled the ration of books/clothing (32:16) what did i do wrong?


The ratio by weight, measured in pounds, of books to clothes to electronics in Jorge's suitcase initially stands at 8 to 5 to 3. Jorge then removes 4 pounds of clothing from his suitcase, thereby doubling the ratio of books to clothes. Approximately how much do the electronics in the suitcase weigh, to the nearest pound?

3
4
5
6


Initially the ratio of B: C: E can be written as 8x: 5x: 3x. (Recall that ratios always employ a common multiplier to calculate the actual numbers.)

After removing 4 pounds of clothing, the ratio of books to clothes is doubled. To double a ratio, we double just the first number; in this case, doubling 8 to 5 yields a new ratio of 16 to 5. This can be expressed as follows:

books

clothing
=

8x

5x - 4
=

16

5




Cross multiply to solve for x:

40x = 80x - 64
40x = 64
x = 8/5

The question asks for the approximate weight of the electronics in the suitcase. Since there are 3x pounds of electronics there are 3 × (8/5) = 24/5 or approximately 5 pounds of electronics in the suitcase.

The correct answer is C.

[tim]

Doubling the ratio of books to clothing does not mean that the new ratio is 2:1; it means the new ratio is twice what it once was. If the ratio started at 8:5, the new ratio is 16:5..

[EricaL474]

Hey Tim,

Thanks for your reply.
I approached the question a bit differently.


Initially, B:C:E = 8:5:3
After Jorge removed 4 pounds of clothing, the ratio of books to clothes doubled. Since the number of books remained the same, the weight should remain the same too.
The new ratio will be B:C:E = 8:4:3
As such, 1 unit = 4 pounds.
Weight of electronics = 3 units = 3x4 = 12 pounds.

May I know what is wrong with my method?

Thanks a lot!

[RonPurewal]

"doubling the ratio" does NOT mean "making the ratio 2:1".

it means changing the ratio into twice its original value.

the initial ratio of books to clothes is 8:5. if you double this ratio, it becomes 16:5 (not 2:1).

[RonPurewal]

by the way—this is the wrong folder for this question.
anything from our materials, besides CAT exams (which have their own folder), belongs in the "MPrep non-CAT math" folder.

since this thread is in the wrong folder, it is now locked. if you have further questions about this problem, please post a new thread in the correct folder.
thanks.