## proportions q.

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### proportions q.

by godemol » Mon Aug 10, 2009 2:43 pm
The only items in a container A are 150 pencils and 725 pens. The ratio of the number of pencils to the number of pens in container B is 2 to 3. If all the pencils and pens in container B are placed in container A, then the ratio of the number of pencils to the number of pens in container A would be 3 to 5. What is the total number of pencils and pens in both container A and container B ?
a.5,600
b.6,725
c.7,125
d.7,275
e.8,000

I've set up the following equations from the question stem:
1. c/n=2/3 (where c=# of pencils in cont. B and n=# of pens in cont. B)
2. (c+150)/(n + 725)=3/5

then, solving for c = 1425, and n=4275. Adding them together, I got 7125, which is choice c. But, the answer is e. 8000. What am i doing wrong?

Thanks.

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by georgeung » Mon Aug 10, 2009 4:08 pm
This is how I did the problem.

Case A: 150/725 (real number)

Case B: 2/3 (ratio)

Combined: (150 + 2x) / (725 + 3x) = 3/5
The reason for the x is because case B is a ratio and we don't know what the real number is.

Now we cross multiply:
3(720 + 3x) = 5(150 + 2x)
2175 + 9x = 750 + 10x
1425 = x

2x + 3x + 150 + 725
2(1425) + 3(1425) + 150 + 725 = 8000

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by ghacker » Mon Aug 10, 2009 4:19 pm
We know that the total number of Pens to pencil ratio for the combined container

The ratio = 3:5 hence the total number must be a multiple of 8

so b , c and d out

Left with a and e

a= 5600 and e = 8000 , but we know the ratio of pens to pencils in container B so a is too low hence the answer is E

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by [email protected] » Tue Aug 11, 2009 11:35 am
Dear Godemol,
You forgot to add the 150 & 725 of container A to your 7125 Ans.

7125 + 875= 8000

Regards

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### niharikamohanty

by godemol » Tue Aug 11, 2009 6:08 pm
niharikamohanty,

wow...thanks...

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by [email protected] » Tue Dec 12, 2017 6:26 am
godemol wrote:The only items in a container A are 150 pencils and 725 pens. The ratio of the number of pencils to the number of pens in container B is 2 to 3. If all the pencils and pens in container B are placed in container A, then the ratio of the number of pencils to the number of pens in container A would be 3 to 5. What is the total number of pencils and pens in both container A and container B ?
a.5,600
b.6,725
c.7,125
d.7,275
e.8,000
We are given that there are 150 pencils and 725 pens in container A.

We are also given that the ratio of pens to pencils in container B is 2 to 3. Thus:

pencils : pens = 2x : 3x

When all of the pens and pencils from container B are placed in container A, the number of pencils in container A becomes 150 + 2x, and the number of pens in container B becomes 725 + 3x. Since the new ratio of pencils to pens is 3 to 5, we have:

(150 + 2x)/(725 + 3x) = 3/5

3(725 + 3x) = 5(150 + 2x)

2175 + 9x = 750 + 10x

1,425 = x

There are 2(1425) = 2850 pencils and 3(1425) = 4275 pens in container B.

Thus, we have a total of 150 + 725 + 2850 + 4275 = 8,000 pens and pencils.