Answer:
The percentage of the components bought from supplier C that are faulty = 88%
Complete Question:
A factory buys 10% of its components from supplier A, 30% from supplier B,and the rest from supplier C. it is known that 6% of the components it buys are faulty. of the components bought from supplier A, 9% are faulty and of the components bought from supplier B, 3% are faulty.
find the percentage of the components bought from supplier C that are faulty ?
Step-by-step explanation:
Let x be the total components bought by the factory
Components supplied by A = 10% of x
Components supplied by B = 30% of x
The rest supplied by C:
Percentage supplied by C = 100-(30+10) = 100-40 = 60%
Components supplied by C = 60% of x
% of all faulty components = 6%
Amount of faulty component = 6% of x
faulty components from A= 9%
Amount of faulty component from A= 9% × (6% of x) = 0.0054x
faulty components from B= 3%
Amount of faulty component from A= 3% × (6% of x) = 0.0018x
Amount of faulty component from C = (6% of x) - (0.0054x+0.0018x)
= 0.06x - 0.0072x
= 0.0528x
Let the percentage of the components bought from supplier C that are faulty = y%
y% × 6% of x = 0.0528x
y% × 0.06x = 0.0528x
y% = 0.0528x/0.06x
y% = 0.88 = 88%
The percentage of the components bought from supplier C that are faulty = 88%
to represent this. Divide both sides by 1/2: