Question

A metal alloy is a metal ade by blending 2 or more type of metal. A jeweler has supplies of two metal alloy 30% gold and the other is 10% gold. How much of each alloy should the jeweler combine to create 4 kg of an alloy containg 15% gold?

Answer 1

1. lets have x= 1 kilogram of the first alloy of 30% gold and y= 1 kilogram of the second alloy of 10% gold.

2. we have to make two equations to solve this problem. for your first one, we can say
x+y=4
this is because both alloys added up must equal 4 kilograms.

3. for your second equation we can say
.3x+.1y=4(.15)

this is because the 30% of gold in the first one added to the 10% of gold in the second one will add up to 15% of gold of the final 4 kilograms.

4. now we can solve using elimination: make one of the variables the opposite of the other

5. first multiply the entire second equation by -10. this is to make the y the opposite of the first equation
-10(.3x+.1y=.6)
-3x-y=-6

6. now since we have positive y in one equation and negative y in the other equation we can add the two equations together to get rid of the y's and find x.

x+y=4 plus
-3x-y=-6
------------
-2x=-2
x=1

7. now that we know what x equals, plug it into the first equation to find y:
1+y=4
y=3.

8 this means your final answer is 1 kilogram of the 30% alloy and 3 kilograms of the 10% alloy :)

Answer 2

thank u very much @pooja195

Answer 3

no problem