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(1) Traditional algebraic approach....
\n" ); document.write( "You are mixing two ingredients to get the final mixture. Find expressions for the amounts of copper in each.
\n" ); document.write( "Ingredient A: x ounces of 20% copper
\n" ); document.write( "The amount of copper is 0.20(x)
\n" ); document.write( "Ingredient B: 300 ounces of 80% copper
\n" ); document.write( "The amount of copper is 0.80(300) = 240
\n" ); document.write( "Mixture: (x+300) ounces of 30% copper
\n" ); document.write( "The amount of copper in the mixture is 0.30(x+300)
\n" ); document.write( "Write and solve the equation that says the amount of copper in the mixture is the sum of the amounts in the two ingredients:
\n" ); document.write( "
\n" ); document.write( "I'll let you finish...
\n" ); document.write( "Note: if you want to avoid calculations with decimals, multiply the whole equation by 10 before doing anything else.
\n" ); document.write( "But here is a faster way to solve mixture problems.
\n" ); document.write( "The ratio in which the two ingredients need to be mixed is exactly determined by how close the percentage of the mixture is to the percentages of each ingredient.
\n" ); document.write( "The mixture percentage, 30, is \"5 times as close to 20 as it is to 80\". That is, 80-30 = 50; 30-20 = 10; the 50 is 5 times the 10.
\n" ); document.write( "That means you need 5 times as much of the 20% copper as the 80% copper.
\n" ); document.write( "Given that there are 300 ounces of the 80% copper, you need 5*300 = 1500 ounces of the 20% copper.
\n" ); document.write( "If you finished solving the problem by the algebraic method shown above, that should be the answer you got. \n" ); document.write( "