A jeweler wants to make 14 grams of an alloy that is precisely 75% gold.. The jeweler has alloys that are 25% gold, 50% gold, & 82% gold. Choose 2 different alloys that can be used to create one that is 75% gold. pls try to explain with a system of equations ; ;

Given that the jeweler has alloys that are 25% gold, 50% gold, and 82% gold.

As he wants to make 14 grams of an alloy by adding two different alloys that is precisely 75% gold, so one alloy must have a percentage of gold more than 75%.

One alloy is 82% gold and, the second can be chosen between 25% gold, 50% gold, so there are two cases.

Case 1: 82% gold + 50% gold

Let x grams of 82% gold and y  grams of 50% gold added to make x+y=14 grams of 75% gold, so

75% of 14 = 82% of x + 50% of y

 [as x+y=14]

grams

and grams.

Hence, 10.9375 grams of 82% gold and 3.0625  grams of 50% gold added to make 14 grams of 75% gold.

Case 2: 82% gold + 25% gold

Let x grams of 82% gold and y  grams of 25% gold added to make x+y=14 grams of 75% gold, so

75% of 14 = 82% of x + 25% of y

grams

and grams.

Hence, 12.28 grams of 82% gold and 1.72  grams of 50% gold added to make 14 grams of 75% gold.

a

step-by-step explanation: