A jeweler wants to make 8 grams of a mixture that is 75% gold. She has an alloy that is 90% gold and an alloy that is 50% gold. How much of each alloy should the dealer use?

Answer: The dealer should use 5 grams of alloy that is 90% gold and a3 grams of alloy that is 50% gold. Step-by-step explanation:Let x be the weight of alloy having 90% gold and y be the weight of alloy having 50% gold .Given : A jeweler wants to make 8 grams of a mixture that is 75% gold. She has an alloy that is 90% gold and an alloy that is 50% gold.According to the above statement , we have the following system of equations :-[tex]\text{Total weight of mixture }: x+y=8-----------------(1)\\\\\text{proportion of gold in mixture}: \dfrac{0.90x+0.50y}{8}=0.75\\\\=0.90x+0.50y=6--------------------(2)[/tex]Multiply 2 on both the sides of equation (2), we get[tex]1.8x+y=12--------------(3)[/tex]Subtract eqn (1) from eqn (3), we get[tex]0.8x=4\\\\\ \Rightarrow\ x=\dfrac{4}{0.8}=5[/tex]Put value of x=5 in (1), we get[tex]5+y=8\\\\ \Rightarrow\ y=8-5=3[/tex]Hence, the dealer should use 5 grams of alloy that is 90% gold and 3 grams of alloy that is 50% gold.