## Sunday, February 15, 2015

### Mathematical Expeditions 2

This is part of an expedition throught the history of word problems. It is adapted from the book Mathematical Expeditions by Frank J. Swetz.

This is a word problem from Renaissance Europe related to shares. Do you dare solving it?

A man had four creditors. To the first he owed 624 ducats; to the second, 546; to the third 492; and to the fourth, 368. It happened that the man defaulted and escaped, and the creditors found that his goods amounted to 830 ducats in all. What will be the share of it?

Explain the procces and the answer using comments. Write your name and course.
END DATE: FEB 22nd

1. creditors are left with 207.5 ducats each

2. I am Jose Luis Barrera. He owed 2030 ducats in all. The creditors had got of his goods 830 ducats. The losses amount to 1200 ducats.
624+546+492+368=2030 ducats.
-2030+830=-1200 ducats.
-1200 ducats is the result.

3. La solucion del problema es cada uno ha ganado 715 ducados.

4. The solution is:
The first creditor has 31% share of it.
The second creditor has 27% share of it.
The third creditor has 24% share of it.
And the fourth creditor has 18% share of it.

Andrea Bretones De Los Rios.

5. Rafael López Vacas 2ºB
Son proporciones directas porque al acreedor que más ducados le debía, más ducados se llevará.
1- El primer acreedor:
2030 830
624 x ; X=(624·830) : 2030= 255,13.
S. Se lleva 255, 13 ducados.
2- El segundo acreedor:
2030 830
546 x ; X=(546·830) : 2030= 223,24.
S. Se lleva 223,24 ducados.
3- El tercer acreedor:
2030 830
492 x ; X=(492·830) : 2030= 201,16.
S. Se lleva 201,16 ducados.
4- El cuarto acreedor:
2030 830
368 x ; X=(368·830) : 2030= 150,46.
S. Se lleva 150,46 ducados.

6. Hello I am Álvaro Mejías Benavente from the class of 2B.
Process: We must to divide 830 ducats among the four creditors.

(x/624)=(y/546)=(z/492)=(w/368)=(830/2030)
(x/624)=(830/2030)
x*2030=830*624; x=(830*624)/2030=255'13 ducats
y=(830*546)/2030=223'24 ducats
z=(830*492)/2030=201'16 ducats
w=(830*368)/2030=150'46 ducats

7. I'm Jose Manuel Muñoz Notario, the first creditor has 255 ducats; the second creditor has 223 ducats; the third creditor 201 ducats and the fourth creditor 151 ducats.
Of total debt (2030) must be found proportionate share of each creditor of a total of 830 real ducats.

The problem is a difficult activity, but I can resolve.

8. Los 830 ducados que el hombre dejo suponían aprox. el 41% de la deuda . Esto lo he hayado multiplicando 830(lo que dejo) por 100(el cien por cien) y dividirlo entre 2030(el total de lo que debe) y esto daría 40,8% que es aproximadamente un 41%. ALBA VILLALBA ROVI.

9. Teacher this is the answer valid, THIS.

ok, this exercise is of rule of three inverse so it is necessary to do:

k+k+k+k/614+546+492+365= 830

1.- 1/684 x/830 (rule of three)= 830/624= 1,33

2.- 1/526 x/830 (rule of three)= 830/546= 1,52

3.- 1/492 x/830 (rule of three)= 830/492= 1,68

4.- 1/365 x/830 (rule of three)= 830/365= 2,27

So, to the first will correspond 1,33 ducats; to the second 1,33; to the third 1,68 ducats and to the fouth 2,27.

10. Thanks for participating and congratulations to Álvaro Mejías and Rafael López. They have found the right answer.