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March 29th, 2019, 07:08 PM  #1 
Newbie Joined: Mar 2019 From: Colombia Posts: 2 Thanks: 0  I'm toasted  please help
Hello everyone, I'm new to the forum, came here looking for a light at the end of the tunnel. I'm not a native speaker so please bear with me. Problem: the whole thing is in Spanish but it pretty much says We want to buy 3 different types of perfume (for men, women and kids) with a budget of 1,500,000.00. We know the cost of the kids perfume is 180,000.00 less than the sum of the other two (men & women) and we know the tax by product is 6% for men perfume, 12% for women perfume and 30% for kids perfume making the invoice 877,200.00 (taxes included). How much money are we going to spend on each perfume type (the high amount is due the currency we got in the country I live in). I do not understand how to correlate these 3 equations to solve the matrix. lets say: X: men perfume Y: women perfume Z: kids perfume then Z: (X+Y)  180,000.00 (this equation would reflect the cost of each perfume). X+Y+Z = 1,500,000.00 (this equation would reflect how much am I going to expend on each perfume type) 1.06X + 1.12Y + 1.3Z = 877,200.00 (this equation would reflect the amount am going to expend on each perfume with taxes) I'm lost.... 
March 29th, 2019, 08:58 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 21,026 Thanks: 2257 
The English version is unclear. Can you post the original Spanish version in full?

March 29th, 2019, 09:30 PM  #3 
Newbie Joined: Mar 2019 From: Colombia Posts: 2 Thanks: 0 
Spanish Version: Se adquieren tres tipos de perfumes. Para hombre, para mujer y para niños, con un presupuesto de 1,500,000.00. El costo del perfume para niños es de 180,000.00 menos que el del hombre y el de la mujer conjuntamente. Se sabe que el IVA por producto es así: 6% perfume para hombre, 12% perfume para mujer y 30% perfume para el de niños, lo que hace que la factura total con impuestos sea 877,200.00. Debes calcular la cantidad de dinero que se va a invertir en cada tipo de perfume. Resolver por el método de Cramer. Translates to: Three types of perfumes are acquired. For men, women and children, with a budget of 1,500,000.00. The cost of perfume for children is 180,000.00 less than that of men and that of women combined. It is known that TAX per product is as follows: 6% perfume for men, 12% perfume for women and 30% perfume for children, which makes the total invoice with taxes 877,200.00. You must calculate the amount of money that will be invested in each type of perfume. Solve by the Cramer method. Last edited by skipjack; March 29th, 2019 at 10:49 PM. 
March 29th, 2019, 11:45 PM  #4 
Global Moderator Joined: Dec 2006 Posts: 21,026 Thanks: 2257 
It doesn't make sense to me. One can't form an equation that includes the budget amount of 1,500,000.00 if the total invoice is only 877,200.00.

March 30th, 2019, 12:40 PM  #5  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1039 
As Skip told you, your problem as stated makes no sense. Your problem as stated is (I included 3 equations): Quote:
Making up an example: [1]: m=530000, w=310000, c = 660000: m + w + c = 1500000 [2]: 660000 = 530000 + 310000  180000 [3]: 1.06m = 561800, 1.12w = 347200, 1.30c = 858000 561800 + 347200 + 858000 = 1767000 So total taxes in this example = 267000. Last edited by Denis; March 30th, 2019 at 12:43 PM.  