Question

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 1

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 :-

$\text{Total weight of mixture }: x+y=8-----------------(1)\\\\\text{proportion of gold in mixture}: \dfrac{0.90x+0.50y}{8}=0.75\\\\=0.90x+0.50y=6--------------------(2)$

Multiply 2 on both the sides of equation (2), we get

$1.8x+y=12--------------(3)$

Subtract eqn (1) from eqn (3), we get

$0.8x=4\\\\\ \Rightarrow\ x=\dfrac{4}{0.8}=5$

Put value of x=5 in (1), we get

$5+y=8\\\\ \Rightarrow\ y=8-5=3$

Hence, the dealer should use 5 grams of alloy that is 90% gold and 3 grams of alloy that is 50% gold.