SOLUTION: You are making 10 tons of concrete that is 62% cement by mixing a 20% cement mixture with a 80% cement mixture. a) How much of the 80% cement mixture must you use? Answer in

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Question 433560: You are making 10 tons of concrete that is
62% cement by mixing a 20% cement mixture
with a 80% cement mixture.
a) How much of the 80% cement mixture
must you use?
Answer in units of tons.
Help me!

Found 2 solutions by lwsshak3, josmiceli:
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
You are making 10 tons of concrete that is
62% cement by mixing a 20% cement mixture
with a 80% cement mixture.
a) How much of the 80% cement mixture
must you use?
..
let x=tons of 80% mixture to use
then 10-x tons of 20% mixture to use
80%x+20%(10-x)=62%(10)
.8x+2-.2x=6.2
.6x=4.2
x=7 tons
ans:
7 tons of 80% mixture is mixed with 3 tons of the 20% mixture to get 10 tons of 62% concrete.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = tons of 20% mixture to be used
Let b = tons of 80% mixture to be used
given:
(1) +a+%2B+b+=+10+ tons
Tons of concrete in 20% mixture = .2a
Tons of concrete in 80% mixture = .8b
(2) +%28.2a+%2B+.8b%29+%2F+10+=+.62+
-------------------------
(2) +.2a+%2B+.8b+=+6.2+
(2) +2a+%2B+8b+=+62+
Multiply both sides of (1) by 2 and
subtract (1) from (2)
(2) +2a+%2B+8b+=+62+
(1) +-2a+-+2b+=+20+
+6b+=+42+
+b+=+7+
and, since
+a%2B+b+=+10+
+a+=+3+
3 tons of 20% mixture are to be used
7 tons of 80% mixture are to be used
check:
(2) +%28.2a+%2B+.8b%29+%2F+10+=+.62+
(2) +%28.2%2A3+%2B+.8%2A7%29+%2F+10+=+.62+
(2) +%28.6+%2B+5.6%29+%2F+10+=+.62+
+6.2%2F10+=+.62+
+6.2+=+6.2+
OK