SOLUTION: problem #1 How many kilograms of each of a 50% silver alloy and 10% silver alloy must be mixed to obtain 24 kilograms of a 25% silver alloy? problem #2 Two vats contain cream, o

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Question 467172: problem #1
How many kilograms of each of a 50% silver alloy and 10% silver alloy must be mixed to obtain 24 kilograms of a 25% silver alloy?
problem #2
Two vats contain cream, one sample tested 8% butterfat and the other tested 16% butterfat. How much cream should be taken from each to produce a 5 liters mixture which will test 12% butterfat?
problem #3
How many kilograms each of a powdered detergent and a rinsing solution containing 80% of the pure rinsing solution must be mixed to make 140 kilograms of a 24% detergent?
I'll be waiting for the answer and solution
Found 2 solutions by Big Poop, Love math:
Answer by Big Poop(157) About Me  (Show Source):
Answer by Love math(28) About Me  (Show Source):
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problem #1
How many kilograms of each of a 50% silver alloy and 10% silver alloy must be mixed to obtain 24 kilograms of a 25% silver alloy?
let x for 50%
let y for 10%
X+y= 24
y= 24-x
0.50x + 0.10y =24*25
substitution y= 24-x
0.50x + 0.10(24-x) = 24*0.25
0.50x + 2.4-0.10x = 24*0.25
0.4x = 6
x=6/0.4
x=15
substitution x= 15 solve for y
X+y= 24
15+y= 24
y =24-15
y =9
nedd 15 for 50%
need 9 for 10%

problem #2
Two vats contain cream, one sample tested 8% butterfat and the other tested 16% butterfat. How much cream should be taken from each to produce a 5 liters mixture which will test 12% butterfat?

let x for 8%
let y for 16%
X+y= 5
y= 5-x
0.08x + 0.16y =5*0.12
substitution y= 5-x
0.08x + 0.16(5-x) =5*0.12
0.08x + 0.8-0.16x = 0.6
-0.08x = 0.6-0.8
x=-0.2/-0.08
x=2.55
substitution x= 2.5 solve for y
X+y= 5
2.55+y= 5
y =5-2.5
y =2.5
nedd 2.5 for 8%
need 2.5 for 16%
roblem #3
How many kilograms each of a powdered detergent and a rinsing solution containing 80% of the pure rinsing solution must be mixed to make 140 kilograms of a 24% detergent?
I'll be waiting for the answer and solution
140 of a 24% =
(140*24)/100 = 33.6
3.6/(140-x)= 80%
(140-x)*80 = 3.6*100
11.200 - 80x = 360
11.200-360 = 80x
10.840/80 = x
135.5 = x