SOLUTION: Sergio found two jars of lemonade in the refrigerator. The first jar contained 8% lemon juice and was to sour. The second jar contained 4% lemon juice and was not sour enough. To m

Question 182524: Sergio found two jars of lemonade in the refrigerator. The first jar contained 8% lemon juice and was to sour. The second jar contained 4% lemon juice and was not sour enough. To make 4 cups of lemonade with 5% lemon juice, how many cups of lemonade did he take from each jar?
How is there a easy way to figure these type of problems. I just can't understand how to get the second equation other than x+y=? or .08x+.04y=.05
Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Sergio found two jars of lemonade in the refrigerator. The first jar contained 8% lemon juice and was to sour. The second jar contained 4% lemon juice and was not sour enough. To make 4 cups of lemonade with 5% lemon juice, how many cups of lemonade did he take from each jar?
How is there a easy way to figure these type of problems. I just can't understand how to get the second equation other than x+y=? or .08x+.04y=.05
------------------------
You almost had it.
But 0.08x is interest on x amt. of money and 0.04y is interest on y amt.
amount of money. But equating that to 0.05, which is simply an interest
rate, does not give you a realistic equality.
---------------------------------------------------
Equation:
interest + interest = interest
0.08x + 0.04(4-x) = 0.05*4
Multiply thru by 100 to get:
8x + 4(4-x) = 5*4
8x + 16 -4x = 20
4x = 4
x = 1 cup (amt. of 8% solution in the mixture)
4-x = 3 cups (amt. of 4% solution in the mixture)
===================================================
Cheers,
Stan H.
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = cups of 4% lemonade needed
Let = cups of 8% lemonade needed
The last sentence tells you how much lemon juice he's
going to end up with
cups of lemon juice in 4 cups
In words:
(cups of lemon juice in 4% lemonade) + (cups of lemon juice in 8% lemonade)
= (.2 cups lemon juice in final mixture)
----------------
given:
(1)
(2)
----------------
from (1)

(2)

and from (1)

He needed 3 cups of the 4% lemonade and 1 cup of the 8% lemonade
check answer:
(2)

OK
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