Question

a clothing manufacturer has some pure silk thread and some thread that is 70% silk. how many kilograms of each must be woven together to make 75 kg of cloth that is 92% silk? pure silk thread kg 70% silk thread kg resources watch it ebook

Explanation:

Step1: Let variables

Let $x$ be the mass of pure - silk thread (100% silk) and $y$ be the mass of 70% silk thread.
We know two equations based on the total mass and the silk - content:

1. Total mass equation: $x + y=75$ (since the total mass of the cloth is 75 kg), so $y = 75 - x$.
2. Silk - content equation: $1.00x+0.70y=0.92\times75$.

Step2: Substitute $y$ into the silk - content equation

Substitute $y = 75 - x$ into $1.00x + 0.70y=0.92\times75$.
We get $x+0.7(75 - x)=0.92\times75$.
Expand the left - hand side: $x + 52.5-0.7x=69$.
Combine like terms: $(x - 0.7x)+52.5 = 69$, $0.3x+52.5 = 69$.

Step3: Solve for $x$

Subtract 52.5 from both sides: $0.3x=69 - 52.5$, $0.3x=16.5$.
Divide both sides by 0.3: $x=\frac{16.5}{0.3}=55$.

Step4: Solve for $y$

Since $y = 75 - x$ and $x = 55$, then $y=75 - 55 = 20$.

Answer:

pure silk thread: 55 kg
70% silk thread: 20 kg