# How many grams of gold should a coin of 35% gold be if when combined with a 3 grams pure gold necklace, it forms a metal that is 69 % gold?

##### 1 Answer

Here's what I got.

#### Explanation:

Since I'm not sure if you're asking for the mass of the

So, let's say that the coin that is **total mass** of **every**

#x color(red)(cancel(color(black)("g coin"))) * "35 g gold"/(100color(red)(cancel(color(black)("g coin")))) = 35/100x " g gold"#

Now let's say that the mass of the

#y color(red)(cancel(color(black)("g coin"))) * "69 g gold"/(100color(red)(cancel(color(black)("g coin")))) = 69/100y" g gold"#

Now, use the **pure gold** coin to write two equations with two unknowns, the mass of gold in the second coin and the total mass of the second coin

#x + 3 = y#

and

#35/100x + 3 = 69/100y#

Use the first equation to get

#x = y - 3#

Plug this into the second equation to get

#35/100 * (y - 3) + 3 = 69/100y#

#35/100y - 105/100 + 3 = 69/100y#

This is equivalent to

#(35 - 69)/100 * y = -195/100#

#34y = 195 implies y = 5.74#

This means that

#x = 5.74 - 3 = 2.74#

So, if you start with a **total mass** of

The first coin will contain

#2.74 color(red)(cancel(color(black)("g coin"))) * "35 g gold"/(100color(red)(cancel(color(black)("g coin")))) = "0.959 g gold"#

I'll leave the values rounded to three sig figs, despite the fact that your values would only justify one sig fig.