Question

You have two small sculptures made of copper and gold. The first sculpture has 5% gold while the second one has 10% gold. The first sculpture has twice the mass of the second one. You melt both, extract the gold and you make a ring of pure gold that is 10 g. What is the mass of the lighter sculpture?

a. 40g
b. 50g
c. 80g
d. 100g
e. 150g

Answer 1

Option b. 50g.

Step-by-step explanation:

We have:

m₁ = is the first sculpture = 5/100 = 0.05

m₂ = is the second sculpture = 10/100 = 0.10

Since the first sculpture has twice the mass of the second one:

`m_(1) = 2*m_(2)` (1)

And, when we melt both sculptures, the ring obtained has 10g:

`0.05m_(1) + 0.10m_(2) = 10 g` (2)

Hence, we have two equations and two variables. By equating equation (1) with (2) we can find the mass of the lighter sculpture:

`0.05(2m_(2)) + 0.10m_(2) = 10 g`

`m_(2) = 50 g`

Hence, m₁ is:

`m_(1) = 100 g`

Therefore, the correct option is b: 50 g is the mass of the lighter sculpture.

I hope it helps you!