Mathematics, 24.07.2019 02:30 unknown5960

Maria has added 2 liters of pure water to 8 liters of a 48% sugar syrup. what is the concentration of the resulting solution?

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We know that
2 liters of pure water = 0 % of sugar
8 liters of syrup = 48% of sugar

Water = (2 liters x 0%) = 0 total sugar liters
Syrup = (8 liters x 48%) = 3.84 total sugar liters
Total liter mix =8+2> 10 liters

Total liters of sugar = 0 + 3.84 = 3.84
if 10 liters> 100%
3.84 liters> x
X=3.84*100/10> x=38.4%

the answer is
38.4%

Answer from: rafaela12

The concentration of the solution, when Maria, added 2 liters of pure water to 8 liters of a 48% sugar syrup is 38.4%.

What is allegation?

Allegation is a method to find the ratio in which two or more indignant are mixed to produce a mixture or solution.

As, Maria added 2 liters of pure water with 8 liters of water, which has 48% sugar syrup. The total amount (in liter) of the mixture is,

$w=8+2\\w=10\rm liters$

Maria has 2 liters of pure water, which has no or zero liters of sugar syrup, and she has 8 liters of water, which has 48% sugar syrup. Therefore, the total amount of sugar syrup is,

$s=0+8\times\dfrac{48}{100}\\s=3.84\rm liters$

There is total 10 liters of water in which 3.84 liters is the amount of sugar syrup. Therefore, the concentration of the resulting solution is,

$c=\dfrac{3.84}{10}\times100\\c=38.4\%$

Hence, the concentration of the solution, when Maria, added 2 liters of pure water to 8 liters of a 48% sugar syrup is 38.4%.

Learn more about the mixture and allegation here;

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Answer from: Quest

The first option would be correct if it were one half and not one

Answer from: Quest

Answer

1 number

explanation

if we use a graphing calculator, there is only one such number $c\in[0.5,0.75]$ that satisfies the conclusion of the mean value theorem, that is, a number $c\in[0.5,0.75]$ such that

$f'(c) = \dfrac{f(0.75) - f(0.5)}{0.75-0.5},$

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.

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Maria has added 2 liters of pure water to 8 liters of a 48% sugar syrup. what is the concentration o...