Question

Tina would like to melt down her existing gold jewelry to make a 20 ounce gold necklace that is 90% pure gold. After melting her jewelry, she is left with two batches. One batch is 75% pure. The other batch is 96% pure. How much of the 96% pure melted gold should Tina mix with the 75% pure melted gold to obtain 20 ounces of 90% pure gold?






A.


5.71 ounces




B.


7.00 ounces




C.


14.29 ounces




D.


13.00 ounces

Answer 1

can i get help from someone pleaese

Answer 2

Let x = amount of 75% pure gold
Let y = amount of 96% pure gold

The total amount of gold she will end up with is 20 ounces, so

x + y = 20

Answer 3

Now let's look at how much actual 100% pure gold she will end up with.

Answer 4

do i divde 96 by all

Answer 5

i dont get it

Answer 6

x ounces of 75% pure gold contain 0.75x ounces of 100% gold.
y ounces of 96% pure gold contain 0.96y ounces of 100% gold.
The final result is 20 ounces of 90% gold, that means 0.90(20) = 18 ounces of 100% pure gold.
This gives us our second equation.

Answer 7

how did you get the 100%

Answer 8

These are the two equations.
x + y = 20
0.75x + 0.96y = 18

Answer 9

Pure gold is 100% gold.
When you say that gold is 75% pure, that means that by weight, 75% of it is gold, and 25% of it is not gold.

Answer 10

oh ok so do i substitute the equations

Answer 11

so half is not gold ok i get it a little bit so what do we do next

Answer 12

Since we used the variable x to mean the amount of 75% gold, the question is how much pure gold is there in x ounces of 75% gold? The answer is 0.75x.

Then we do the same for the 96% gold. 0.96y is the amount of pure gold in y ounces of 96% gold.

Finally we do the same for the end result. The end result after mixing is 20 ounces of 90% gold. Here we actually know that the weight is 20 ounces, so the amount of pure gold in it is 90% of 20 oz or 0.9 * 20 = 18 ounces.

Then we add the amounts of pure gold, and it must equal 18:

0.75x + 0.96y = 18
That's how we get the second equation.

Answer 13

i got the wrong answer what did u get i got 14.29 ounces

Answer 14

Ok, back to solving the problem.

We have this system of equations.

x + y = 20
0.75x + 0.96y = 18

We can use substitution.
We can solve the first equation for one variable, let's say x, then substitute into the second equation.

Answer 15

Which variable is equal to 14.29?

Answer 16

i got it right yay thank you so much

Answer 17

Great. You're welcome.

Answer 18

did i get it right im not sure

Answer 19

You didn't answer my question. Which variable did you get 14.29 ounces for? x or y?

Answer 20

oh no i thought i got the answer right im sorry

Answer 21

thank you so much

Answer 22

x = 20 - y
0.75(20 - y) + 0.96y = 18
15 - 0.75y + 0.96y = 18
15 + 0.21y = 18
0.21y = 3
y = 14.29

Now substitute y = 14.29 in x + y = 20 to find x.
x + 14.29 = 20
x = 5.71

Answer: 5.71 oz of 75% gold and 14.29 oz of 96% gold.

Answer 23

You're welcome.