Ratio of stamps

[manjeshmurthy]

Hello Instructors,

before posting this i tried searching for this problem couldn't find one
source from mba.com practice test

Number of stamps that kaye & albero had were 5:3, after Kaye gave Alberto 10 of her stamps. the ratio of number of stamps kaye had to number of stamps alberto had was 7:5. As a result of this gift, kaye had how many more stamps than alberto

a) 20 b) 30 c) 40 d)60 e) 90

i tried solving by (5x-10)/(3x-10) = 7/5 , where i got x = 5, but was not sure how to proceed further or the approach is right

so can you guys show the way to solve this

[emailnaik]

i tried solving by (5x-10)/(3x-10) = 7/5 , where i got x = 5

x cannot be equal to 5 since from your given equation
(5x-10)/(3x-10) = 7/5
25x-50=21x+70
25x-21x=70+50 (note that you have to add 50 on both the sides and subtract 21x from both the sides)

[agha79]

Can you Tell me what the answer is?

I setup the problem to show unknown multiplier.

(5x -10) / (3x + 10) = 7/5
25x - 50 = 21x + 70
4x = 120
x = 30

Now found the orginal quntity

Kaye = 5 x 30 = 150
Albero = 3 x 30 = 90

Kay gave Alberto 10 of her stamps so now Kaye has (150 - 10) = 140 stamps and Albero has (90 + 10) = 100 stamps.

Question Asks us "As a result of this gift, kaye had how many more stamps than alberto"

so we need to subtract Alberto's new stamp qunitity (100) from Kayes new stamp quntity (140)

140 - 100 = 40

My answer is "C"
Can you please confirm if this is the right answer?

[manjeshmurthy]

oh wow..you guys made this problem look so easy...
i screwed up the calculation but glade that my approach was correct.

Yes the answer is very correct, its "C" 40

[dmitryknowsbest]

Great responses, folks.

To address your original question, Manjesh, the problem breaks down into 4 parts:

1) Express the given information in a proportion equation using the unknown multiplier. (This is what you did, except you put -10 instead of +10 on the bottom.)

2) Cross-multiply and solve for x. This is where you need to be more careful. It looks like you set the denominators of the two sides equal to each other. (3x - 10 = 5). You can't do this, because the part on the bottom doesn't necessarily equal 5; it is just 5/7 of the part on the top. We end up with x=30.

3) Once you solve for x, go back and find the actual values. I think this is what you were asking about. You just plug the unknown multiplier back into the ratio expression, as agha demonstrated. Since we are looking for the values after Kaye gave the stamps to Alberto, we can simply use 5x-10 and 3x+10 to find those values. 5(30) - 10 = 140 and 3(30) + 10 = 100.

4) To finish off, we need to answer the exact question asked. The problem asks for the difference between the current values, so we get 140-100 = 40.

So yes, do watch for those math errors, but also make sure you have a plan to solve. Otherwise, you will spend a lot of time making frustrated marks on your scratch paper!