Assume all 9 are $1 coins first.

Total mass = 7.62g x 9 = 68.58g

Now this is higher than 42.19g. So we need to replace some $1 coins with 20¢ coins.

7.62g - 3.85g = 3.77g

For every $1 coin you replace with a 20¢ coin, it causes the total mass to go down by 3.77g

68.58g - 42.19g = 26.39g

Since there is a decrease of 26.39g,

26.39g ÷ 3.77g = 7

So we have to replace 7 $1 coins . This tells you that there are actually 7 20¢ coins

So 9 - 7 = 2

There are 2 $1 coins.

nos.
$1: u
20c: 9-u


mass
$1: 7.62xu = 7.62u
20c: 3.85x(9-u) = 34.65 - 3.85u

total mass = 7.62u + 34.65 - 3.85u
= 34.65 + 3.77u


34.65 + 3.77u = 42.19
u = 2

2 $1
7 20c


...

Many thanks