Question 1196993: A clothing manufacturer has some pure silk thread and some thread that is 80% silk. How many kilograms of each must be woven together to make 60 kg of cloth that is 95% silk?
pure silk thread=__________ HOW Much KG?
80% silk thread= _________ HOW Much KG?
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
I'll label the threads A,B,C
Thread A = pure silk, aka 100% silk
Thread B = 80% silk thread
Thread C = 95% silk
The clothing manufacturer has thread A and thread B, but they don't have thread C.
The goal is to somehow mix the two given threads (A & B) to get thread C.
Let
x = amount of thread A, in kg
Since we want 60 kg of thread C, this means 60-x represents the amount of thread B in kg.
The expressions x and 60-x add to 60.
Thread A is pure silk, so we have x kilograms of pure silk so far.
Thread B is 80% silk, which means we contribute another 0.80(60-x) = 48-0.80x kilograms of pure silk onto the x already there.
A+B = (x)+(48-0.80x) = 48+0.20x = total amount of pure silk.
Divide this over the 60 kg of total fabric, and we want this ratio to be 0.95 due to the 95% target rate.
(amount of pure silk)/(amount of fabric total) = 95% silk
(48+0.20x)/(60) = 0.95
Let's solve for x.
(48+0.20x)/60 = 0.95
48+0.20x = 60*0.95
48+0.20x = 57
0.20x = 57-48
0.20x = 9
x = 9/0.2
x = 45
We need 45 kg of thread A (the pure 100% silk)
and we need 60-x = 60-45 = 15 kg of thread B (the 80% silk)
100% of 45 = 45 kg of pure silk is from thread A
80% of 15 = 0.8*15 = 12 kg of pure silk is from thread B
We get 45+12 = 57 kg of pure silk out of 60 kg total
57/60 = 0.95 = 95% so we've reached the proper target.
Answers
pure silk thread = 45 kg
80% silk thread = 15 kg
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Another approach:
The target is 95%
The gap from 100% to 95% is 5 percentage points
The gap from 80% to 95% is 15 percentage points
We write the results in reverse order to get the ratio 15:5 which reduces to 3:1
This tells us we need 3 times as much of the pure silk compared to the 80% silk
This is because the 3 is listed first and the pure silk is listed first.
n = some unknown positive real number
The ratio 3:1 scales up to 3n:1n
These two parts must add to 60 kg total
3n+1n = 60
4n = 60
n = 60/4
n = 15
We need 3n = 3*15 = 45 kg of the pure silk and 1n = 1*15 = 15 kg of the 80% silk
Answers
pure silk thread = 45 kg
80% silk thread = 15 kg
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