How many pounds of an $83 per pound substance must be mixed with an $11 per pound substance to get 240 lbs of an alloy which will cost $28 per pound? Round to the nearest pound.

57 lbs

183 lbs

205 lbs

35 lbs

Question

How many pounds of an $83 per pound substance must be mixed with an $11 per pound substance to get 240 lbs of an alloy which will cost $28 per pound? Round to the nearest pound.
 
		
57 lbs
 		
183 lbs
 		
205 lbs
 		
35 lbs

jewlzme17 · Answer

x = lbs of $83
 
y = lbs of $11
 
You have two unknowns, so you need two equations
 
x + y = 240 lbs
 
&
 
(83x + 11y)/240 = $28 or 83x + 11y = 6720
 
Change the first equation to y = 240 - x
 
Now plug it into the second equation 83x + 11(240 - x) = 6720
 
so 83x + 2640 - 11x = 6720
 
so 72x = 4080
 
so x = 56.67, so the answer is a.