SOLUTION: I don't even know where to begin on this problem. This is a question from my college Algebra 2 course. A precious metals company receives an order for a block of 160 lbs. of al

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Question 353420: I don't even know where to begin on this problem. This is a question from my college Algebra 2 course.
A precious metals company receives an order for a block of 160 lbs. of alloy which is 35% silver. The block is made from two individual blocks. The first individual block was 50% silver. The second individual block was 25% silver. What were the weights of the two original blocks?
Answer by Earlsdon(6294) (Show Source):
You can put this solution on YOUR website!
Think about the amount of silver in each of the blocks of alloy.
The 160-lb block has 35% of 160 lbs of silver, or (0.35)(160) lbs of silver.
The two blocks from which this is made have x(0.5) lbs of silver and (160-x)(0.25) lbs of silver. x is the weight of the block with 50% silver.
So we set these quantities equal.
(0.35)(160) = x(0.50)+(160-x)(0.25) Simplify and solve for x.
56 = 0.5x+40-0.25x Subtract 40 from both sides.
16 = 0.5x-0.25x Simplify.
16 = 0.25x Divide both sides by 0.25
64 = x and...
160-x = 96
The weights of the original blocks were:
64 lbs of the 50% silver alloy and 96 lbs of the 25% silver alloy.