Please help with this word problem..

Question

a merchant bought 12 dressers and 10 coats for $640. She sold the dresses at a profit of 40% and the coats at a profit of 30% and received in all $856. Find the cost of each dress and each coat.

Answer 1

12d + 10c = 640

12(1.4)d + 10(1.3c) = 856

 

Can you solve the system?

Answer 2

X = Price of Dress and Y = Price of coat
12X + 10Y = 640 (EQ1)
40% Profit on X is X + 0.4X = 1.4X and a 30% Profit on Y is Y + 0.3Y = 1.3Y
12 (1.4X) + 10 (1.3Y) = 856 which is 16.8X + 13Y = 856 (EQ2)

Use Elimination – to eliminate the Y’s, Multiply EQ1 By 13 and Multiply EQ2 By 10
The new EQ2 is 168X + 130Y = 8560
The new EQ1 is 156X + 130Y = 8320
Then Subtract EQ1 from EQ2 to get 12X=240 and X=20. Put X=20 into the original EQ1 to get 12(20) + 10Y = 640 so 10Y = 400 and Y=40.
If the merchant paid 20 for the dress, then the 40% markup is 8 for a sold price of 28. If the merchant paid 40 for the coat, then the 30% markup is 12 for a sold price of 52. The dress cost 28 and the coat cost 52.
The 12 dresses were sold for 336 (12x28) and the 10 coats were sold for 520 (10x52) which gives the 856 (336+520) total.