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?

Answer 1

I can surely help you with this! You need a table for this to keep things in order so let me insert one.
In order to fill in this table, you need to use the info you're given in the problem, keeping in mind the final product will weigh 20 ounces and will be 90% pure. If you are mixing A with B, then we find some values for those. The first thing we are going to do is fill in the last row, the final product. The amount of gold she is looking at is 20 ounces, so "20" goes in that box. The percent she wants that gold to be is 90%, so .90 would go in that box. Now we will move up to batch A and B. If batch A is 75% pure, what is the decimal that would go in that % gold box (.75). And the same for batch B. What % is batch B? (96%. So .96 goes in that box.). Now this is the part where many of my Algebra students got stuck. What numbers go into the amt gold box? Well, if the final result is to be 20 ounces and you don't know how much of A or B you have, then they are both unknown. Since they can't both be x, and they need to add up to = 20, one would be x and the other would be 20 - x. For example, if x was 16 ounces, then 20 - x would be 4 ounces, because 16 and 4 add up to give you 20. So you have to find an x and then subtract it from 20 to give you the second amount. When you have the boxes in your table filled out, it will look like this.Each of these rows needs to be multiplied straight across to fill in the final column, the third column. See if you can work with that. When you fill in the third column, you need to add the first two boxes and set them to = the last box. That column is the third one, going down. You need those values, that column is the solutions column. If you are still stuck, I will help you after I get home from church!