SOLUTION: Okay, I really just need an equation to understand this; Jessica mixed 5 oz of soil containing 26% clay with 6oz of soil with 14% clay. What is the content of the mixture? Also

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Okay, I really just need an equation to understand this; Jessica mixed 5 oz of soil containing 26% clay with 6oz of soil with 14% clay. What is the content of the mixture? Also      Log On


   



Question 945241: Okay, I really just need an equation to understand this;
Jessica mixed 5 oz of soil containing 26% clay with 6oz of soil with 14% clay. What is the content of the mixture?
Also... Nancy mixed 10 L of cranberry juice into 13 L of apple juice, that had 50% sugar content. If the cranapple mixture is 42% sugar! what was the percent of sugar in the cranberry juice?

Found 2 solutions by macston, josmiceli:
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
1.CLAY
5 oz of soil at 26% clay=5oz(.26)=1.3 oz clay
6 oz of soil at 14% clay=6oz(.14)=0.84 oz clay
We have 5 oz + 6 oz =11 oz total with 1.3+0.84=2.14 oz of clay
(2.14 oz/11 oz)(100%)=19.5% clay
ANSWER The combined soils are 19.5% clay
2.FRUIT JUICE
The 23 L is 42% sugar, so there is 0.42(23L)=9.66 sugar
The 13L apple juice at 50% had 0.50(13L)=6.50 sugar
So of the 9.66 sugar in the blend, 6.50 came from apple juice so
9.66-6.50=3.16 sugar came from the 10 L of cranberry juice
(3.16/10L)(100%)=31.6% sugar in the original cranberry juice

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+.26%2A5+=+1.3+ ounces of clay in 26% soil
+.14%2A6+=+.84+ ounces of clay in 14% soil
+1.3+%2B+.84+=+2.14+
The mixture has 2.14 ounces of clay
---------------------------------
They want the % sugar in the cranberry
mixture
Let +x+ = liters of sugar in the cranberry juice
+.5%2A13+=+6.5+ liters of sugar in apple juice
+%28+x+%2B+6.5+%29+%2F+%28+10+%2B+13+%29+=+.42+
+x+%2B+6.5+=+.42%2A23+
+x+=+9.66+-+6.5+
+x+=+3.16+
---------------
What you want is ( liters of sugar in cranberry ) / ( liters of cranberry )
multiplied by +100+
+%28+3.16+%2F+10+%29%2A100+=+31.6+
31.6% sugar in cranberry juice
--------------------------
check:
+%28+x+%2B+6.5+%29+%2F+%28+10+%2B+13+%29+=+.42+
+%28+3.16+%2B+6.5+%29+%2F+%28+10+%2B+13+%29+=+.42+
+3.34+%2F+23+=+.42+
+9.66+=+9.66+
OK