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Lotmonade Inc. produces lemonade: a mixture of sugar and lemon juice , 13 Jan 2022, 02:45
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Lotmonade Inc. produces lemonade: a mixture of sugar and lemon juice ,with varying sugar content ,at $7.95/litre. The lemonade contains 7% sugar.Another lemonade containing 75% lemon juice costs $8.10/litre. How much does Jessica pay for 6 liters of a lemonade containing 12% sugar?

A. $84.84
B. $79.92
C. $74.94
D. $47.94
E. None of these



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Lotmonade Inc. produces lemonade: a mixture of sugar and lemon juice , 04 Mar 2022, 08:10
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Let the amount of $7.95/litre of lemonade with 7% sugar = x
Let the amount of $8.10/litre of lemonade with 25% sugar = y

0.07x + 0.25y = 0.12(x+y)
0.13y = 0.05x
\(\frac{x}{y}\) = \(\frac{13}{5}\)

13k+5k = 18k
18k = 6 litres
k = \(\frac{1}{3}\)

Total amount to be paid = \(\frac{13}{3}*7.95 + \frac{5}{3}*8.10\) = $ 47.95 (D)
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Lotmonade Inc. produces lemonade: a mixture of sugar and lemon juice , 16 Jan 2022, 16:46
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In order to make a solution with 12% and 88% lemonade, we will need 4 and 1/3 litres of the $7.95/litre lemonade which has 7% sugar and 1 and 2/3 litres of the $8.10 lemonade which has 25% sugar. This will give us 6 litres of lemonade with 12% sugar and 88% lemonade. The sum for this comes to $47.95 which is not one of the answer choices. The closest is $47.94 but that is off by 1 cent. So, I am going to wait for the official solution.
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Lotmonade Inc. produces lemonade: a mixture of sugar and lemon juice , 06 Sep 2023, 10:07
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bv8562
Let the amount of $7.95/litre of lemonade with 7% sugar = x
Let the amount of $8.10/litre of lemonade with 25% sugar = y

0.07x + 0.25y = 0.12(x+y)
0.13y = 0.05x
\(\frac{x}{y}\) = \(\frac{13}{5}\)

13k+5k = 18k
18k = 6 litres
k = \(\frac{1}{3}\)

Total amount to be paid = \(\frac{13}{3}*7.95 + \frac{5}{3}*8.10\) = $ 47.95 (D)
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Hi, I would like to ask how you came up with the 13k + 5k = 18k? What exactly should k be? Thank you!
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Lotmonade Inc. produces lemonade: a mixture of sugar and lemon juice , 06 Sep 2023, 23:28
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JoeSal
bv8562
Let the amount of $7.95/litre of lemonade with 7% sugar = x
Let the amount of $8.10/litre of lemonade with 25% sugar = y

0.07x + 0.25y = 0.12(x+y)
0.13y = 0.05x
\(\frac{x}{y}\) = \(\frac{13}{5}\)

13k+5k = 18k
18k = 6 litres
k = \(\frac{1}{3}\)

Total amount to be paid = \(\frac{13}{3}*7.95 + \frac{5}{3}*8.10\) = $ 47.95 (D)

Hi, I would like to ask how you came up with the 13k + 5k = 18k? What exactly should k be? Thank you!
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JoeSal Since \(\frac{x}{y}\) is a ratio, 'k' is the ratio multiplier (a constant). If we are given a ratio like \(\frac{x}{y}\) = \(\frac{13}{5}\) then it doesn't mean that x=13 and y=5. But what it actually means is that no matter what is x and y, when \(\frac{x}{y}\) is reduced to the lowest terms, it turns out to be \(\frac{13}{5}\). Thus, \(\frac{x}{y}\) could be \(\frac{13}{5}\) or \(\frac{26}{10}\) or \(\frac{39}{15}\) etc. In order to show this relationship between two variables in a ratio we use a constant such as 'k'. The whole idea is that the constant will get cancelled out and the ratio will turn out to be the same. I hope it helps.
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Lotmonade Inc. produces lemonade: a mixture of sugar and lemon juice , 06 Sep 2023, 23:54
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Bunuel
Lotmonade Inc. produces lemonade: a mixture of sugar and lemon juice ,with varying sugar content ,at $7.95/litre. The lemonade contains 7% sugar.Another lemonade containing 75% lemon juice costs $8.10/litre. How much does Jessica pay for 6 liters of a lemonade containing 12% sugar?

A. $84.84
B. $79.92
C. $74.94
D. $47.94
E. None of these



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Cost of 7% sugar solution is $7.95/litre
Cost of 25% sugar solution is $8.10/litre

To make 12% sugar solution, use the formula or number line:

\(\frac{w1}{w2} = \frac{(A2 - Aavg)}{(Avg - A1)} = \frac{(25 - 12)}{(12 - 7)} = \frac{13}{5}\)

So ratio of the weights of the two sugar solutions will be 13:5 to give a 12% sugar solution.
If we need 6 ltrs of 12% sugar solution, since total of 13 + 5 is 18 on ratio scale, it means the multiplier is 1/3 so the actual value of the two amounts will be 13/3 ltrs and 5/3 ltrs.

Total cost will be \(\frac{13}{3 }* 7.95 + \frac{5}{3} * 8.10 = $47.95\)

Answer (D)

Check Weighted Avg and Mixtures Basics here:
https://anaprep.com/arithmetic-weighted-averages/
https://anaprep.com/arithmetic-mixtures/
and these videos:
https://www.youtube.com/watch?v=_GOAU7moZ2Q
https://www.youtube.com/watch?v=VdBl9Hw0HBg
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Lotmonade Inc. produces lemonade: a mixture of sugar and lemon juice , 17 Sep 2025, 22:23
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