2. A set of barbells consist of red and blue discs. Discs with the same color have the same mass. Using a balance, Lia found that 7 blue discs balance 1 red disc and a 5kg mass, while 2 blue discs and a red disc balance a 4kg
mass. Find the masses of the red and blue discs. (2kg, 1kg)

Let r be the mass of a red disc and b the mass of a blue disc.

7 blues have the same mass as 1 red along with a 5 kg mass, so

7b = r + 5

7b - r = 5

2 blues and 1 red have the same mass as a 4 kg mass, so

2b + r = 4

Solve for b and r . Notice that adding the equations together eliminates r :

(7b - r) + (2b + r) = 5 + 4

9b = 9

b = 1

Then

7 • 1 - r = 5

r = 7 - 5

r = 2

So each red disc has a mass of 2 kg, and each blue disc has a mass of 1 kg.