please help :o How many lb. of a metal containing 10% gold must be combined with 7 lb. of a metal containing 70% gold to form an alloy containing 52% gold?
if you have 7 lbs of metal, and 70% of it is gold, then it is 0.70*7 lbs of gold. same logic with the 10% metal. we don't know how much of the 10% metal we need, but we know it has 0.10*x lbs of gold together, this is 0.70*7 + 0.10x lbs of gold. in total, we have x + 7 lbs of gold so far. we know we want a 52% gold alloy. so we know that (amount of gold) / (amount of metal) * 100% must equal 52%. so our equation is (0.70*7 + 0.10x)/(x+7) = 0.52 and you can solve for x from here
where does x + 7 come from
we have: 7 lbs of the 70% alloy some unknown x lbs of the 10% alloy so total amount of metal = x + 7
should be have x + 7 lbs of total metal, not gold, that was my mistake
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