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

Option C is the answer.

Step-by-step explanation:

Let 96% pure gold  be represented by x

Let 75% pure gold  be represented by y

Tina would like to melt down her existing gold jewelry to make a 20 ounce gold necklace that is 90% pure gold.

So, equation forms :

or     ....(1)

Now mixing 96% pure melted gold and the 75% pure melted gold to obtain 20 ounces of 90% pure gold is given by:

=>     .....(2)

Substituting the value of x from equation 1 in 2.

And x=20-y

So,

So, Tina should mix 14.29 ounces of 96% pure gold.

step-by-step explanation:

step 1: solve one of the equations for one of the variables. let's solve the first equation for y:

step 2: substitute that equation into the other equation, and solve for x.

step 3: substitute x = 4 x = 4 x=4 into one of the original equations, and solve for y.