SOLUTION: Emir, Cillian, and Lasha are avid collectors of vintage postage stamps. During a local exhibition, they decided to donate parts of their collections to a museum. The ratio of the n

Question 1210616: Emir, Cillian, and Lasha are avid collectors of vintage postage stamps. During a local exhibition, they decided to donate parts of their collections to a museum. The ratio of the number of stamps Emir and Cillian gave away was 4:7, while the ratio of the number of stamps Cillian and Lasha gave away was 3:5. The number of stamps Emir gave away was 20 fewer than the number of stamps he kept for himself. Cillian kept 3/2 as many stamps as Emir kept, and Lasha kept 4/3 as many stamps as Cillian kept. After their donations, they had a combined total of 738 stamps left in their collections. How many stamps did Lasha give away?
Found 3 solutions by KMST, ikleyn, MathTherapy:
Answer by KMST(5361)   (Show Source): You can put this solution on YOUR website!
EDIT: My calculations are wrong. See The much clearer and direct solution by iklein.
For every 4 stamps donated by Emir, there were 7 stamps donated by Cillian.
For every 3 stamps donated by Cillian, there were 5 stamps donated by Lasha.
That means that for every stamps given away by Cillian, there were
stamps given away by Emir, and
This is wrong --> stamps given away by Lasha.
It should have been .

Let us make
the number of stamps donated by Emir ,
the number of stamps given by Cillian , and
the number of stamps given by Lasha ,

EDIT:Here is where the other solutions are better (besides having no mistakes). I insisted on calculating number of stamps kept based on , but that unnecessarily complicates the calculations.
The number of stamps Emir gave away was 20 fewer than the number of stamps he kept for himself means Emir kept stamps. See the much clearer and direct solution by Iklein.
Cillian kept 3/2 as many stamps as Emir, Cillian and Lasha kept means
Cillian kept stamps.

Lasha kept 4/3 as many stamps as Cillian kept means
Lasha kept stamps.
After their donations, the total number of stamps Emir, Cillian and Lasha had left in their collections was
<-->-->-->-->-->-->

Lasha gave away stamps.

In table form that looks like:
-->
After solving ->->-> , we can substitute that value to get

We can calculate the number of stamps each one originally had, and the number each donated,
but we are only asked for the number Lasha donated: .
Answer by ikleyn(53846)   (Show Source): You can put this solution on YOUR website!
.
Emir, Cillian, and Lasha are avid collectors of vintage postage stamps.
During a local exhibition, they decided to donate parts of their collections to a museum.
The ratio of the number of stamps Emir and Cillian gave away was 4:7,
while the ratio of the number of stamps Cillian and Lasha gave away was 3:5.
The number of stamps Emir gave away was 20 fewer than the number of stamps he kept for himself.
Cillian kept 3/2 as many stamps as Emir kept,
and Lasha kept 4/3 as many stamps as Cillian kept.
After their donations, they had a combined total of 738 stamps left in their collections.
How many stamps did Lasha give away?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Let' start from this point "The ratio of the number of stamps Emir and Cillian gave away was 4:7, while the ratio of the number of stamps Cillian and Lasha gave away was 3:5." We want to write this statement as a long proportion of three terms. For it, write partial proportions E:C = 4:7 and C:L = 3:5 as long three terms proportion E:C:L = 12:21:35. The logic for it is that 4:7 is the same as 12:21 (after multiplication by 3), while proportion 21:35 is the same as 3:5 (after dividing by 7). So, we can assume that Emir gave away 12x stamps, Cillian gave away 21x stamps and Lasha gave away 35x stamps. Next, let E be the number of stamps Emir kept. Then the number of stamps Cillian kept was , and the number of stamps Lasha kept was = 2E. We are given that the combined total number of stamps left in their collection was 738. So, we write this equation E + + 2E = 738. Hence 2E + 3E + 4E = 738*2, 9E = 1476, E = 1476/9 = 164. Now, the problem says "The number of stamps Emir gave away was 20 fewer than the number of stamps he kept for himself." It means that 12x = 164 - 20. From it, we find 12x = 144, x = 144/12 = 12. Very good. Now we are in position to find the number of stamps Lasha gave away. It is 35x = 35*12 = 420. ANSWER. Lasha gave away 420 stamps.

Solved completely.

Answer by MathTherapy(10837)   (Show Source): You can put this solution on YOUR website!

Emir, Cillian, and Lasha are avid collectors of vintage postage stamps. During a local exhibition, they decided to donate parts of their collections to a museum. The ratio of the number of stamps Emir and Cillian gave away was 4:7, while the ratio of the number of stamps Cillian and Lasha gave away was 3:5. The number of stamps Emir gave away was 20 fewer than the number of stamps he kept for himself. Cillian kept 3/2 as many stamps as Emir kept, and Lasha kept 4/3 as many stamps as Cillian kept. After their donations, they had a combined total of 738 stamps left in their collections. How many stamps did Lasha give away? ************************************************************************** Emir: E Cillian: C Lasha: L Ratio of E:C = 4:7 Ratio of C:L = 3:5 Since C (Cillian) obviously gave away the same amount, the ratios can be changed from E:C = 4:7 to: 4(3):7(3) = 12:21, and from C:L = 3:5 to 3(7):5(7) = 21:35 We now have the ratio of the 3 donors as: E:C:L = 12:21:35 As such, E(Emir), C(Cillian), and L(Lasha) gave away 12x, 21x, and 35x stamps, respectively, with x being the MULTIPLICATIVE FACTOR Since the number of stamps Emir gave away was 20 FEWER than the number of stamps he kept for himself, he kept 20 MORE than he donated, or 12x + 20 And, as Cillian kept as many stamps as Emir did, the number Cillian kept was = 18x + 30 Now, since Lasha kept as many as Cillian, Lasha kept = 24x + 40 stamps As they had a combined 738 stamps left in their collections, we get the following TOTAL remaining-stamps equation: 12x + 20 + 18x + 30 + 24x + 40 = 738 54x + 90 = 738 54x = 648 MULTIPLICATIVE factor, or x = = 12 Lasha gave away 35x stamps (see above), or 35(12) = 420 stamps

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