Problem Solving

alex.gellatly wrote: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?

Ratio of books to clothes = 8:5

Say, weight of books and clothes are 8x and 5x respectively, in pounds.

So, 8x/(5x - 4) = 16/5
--> 40x = 80x - 64
--> 40x = 64
--> x = 8/5

Therefore, weight of electronics in the suitcase = 3*(8/5) = 24/5 ≈ 5

The correct answer is C.

alex.gellatly wrote: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
7

We are given that the ratio of books to clothes to electronics in Jorge's suitcase initially stands at 8 to 5 to 3 or 8x : 5x : 3x. We are also given that Jorge removes 4 pounds of clothing from his suitcase, thereby doubling the ratio of books to clothes. We see that the original ratio of books to clothes was 8/5, so a ratio doubling that would be 16/5. So, we have:

8x/(5x - 4) = 16/5

5(8x) = 16(5x - 4)

40x = 80x - 64

64 = 40x

64/40 = 8/5 = x

Thus, the weight of the electronics is 3(8/5) = 24/5 = about 5 pounds.

Answer: C