SOLUTION: Your assistance is greatly appreciated. Angela needs 20 quarts of 50% antifreeze solution in her radiator. She plans to obtain this by mixing some pure antifreeze with an app

Algebra ->  Customizable Word Problem Solvers  -> Mixtures -> SOLUTION: Your assistance is greatly appreciated. Angela needs 20 quarts of 50% antifreeze solution in her radiator. She plans to obtain this by mixing some pure antifreeze with an app      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 57310This question is from textbook Elementary and Intermediate algebra
: Your assistance is greatly appreciated.
Angela needs 20 quarts of 50% antifreeze solution in her radiator. She plans to obtain this by mixing some pure antifreeze with an appropriate amount of 40% antifreeze solution. How many quarts of each should she use? This question is from textbook Elementary and Intermediate algebra

Found 3 solutions by aaaaaaaa, CrazyMan Jr., ptaylor:
Answer by aaaaaaaa(138) About Me  (Show Source):
You can put this solution on YOUR website!
p = quarts of pure antifreeze sol.
i = quarts of the impure one
The second equation needs some explanation, 50% of 20 is 10.
system%28p+%2B+i+=+20%2C+p+%2B+0.4i+=+10%29
Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
+system%28+%0D%0A++++1%5Cp+%2B+1%5Ci+=+20%2C%0D%0A++++1%5Cp+%2B+0.4%5Ci+=+10+%29%0D%0A++We'll use substitution. After moving 1*i to the right, we get:
1%2Ap+=+20+-+1%2Ai, or p+=+20%2F1+-+1%2Ai%2F1. Substitute that
into another equation:
1%2A%2820%2F1+-+1%2Ai%2F1%29+%2B+0.4%5Ci+=+10 and simplify: So, we know that i=16.6666666666667. Since p+=+20%2F1+-+1%2Ai%2F1, p=3.3333333333333.

Answer: system%28+p=3.3333333333333%2C+i=16.6666666666667+%29.

Answer by CrazyMan Jr.(21) About Me  (Show Source):
You can put this solution on YOUR website!
0.4x+1x = 0.5
x+y = 20

0.4x+1y = 0.5 0.6y = -7.5 y = -12.5
0.4x+0.4y = 8 0.6y/0.6 = -7.5/0.6
Sub In
0.4x+1(-12.5) = 0.5
0.4x(+-)12.5 = 0.5
0.4x-12.5(+12.5) = 0.5(+12.5)
0.4x = 13
0.4x/0.4 = 13/0.4
x = 32.5
Proof - Sub In Again
0.4(32.5)+1(-12.5) = 0.5
13+-12.5 = 0.5
0.5 = 0.5
N.P.
J-Man

Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=amt of pure antifreeze that is mixed in
Then 20-x=amt of 40% antifreeze solution that is mixed in
We know that the amt of pure antifreeze that is mixed in (x)(1) plus the amt of pure antifreeze in the 40% solution that is mixed in (20-x)(.40) equals the amt of pure antifreeze in the final solution (20)(.50).
Thus, our equation to solve is:
(x)(1)+(20-x)(.40)=(20)(.50) Simplifying, we get:
x+8-.4x=10 or
.6x=2; 6x=20
x=3.3333 qts of pure antifreeze
20-x=20-3.3333=16.6667 qts of the 40% antifreeze solution
Hope this helps-----ptaylor