Question

One half liter of lemonade concentrate is added to 3 liters of water. How many $ \dfrac{1}{3} $ liter servings of lemonade are made?

Answer 1

Hint: In such questions where we are given an algebraic word problem to solve, we first write the given word problem in terms of mathematical equations and then solve it using the algebraic operations. Algebraic rules such as transposition are of much use to solve algebraic word problems as one given in the question.

Complete step by step solution:
Volume of lemonade concentrate $ = 0.5 $ liter
Volumes of water to be added $ = 3 $ liters
Total volume of lemonade mixture $ = 3.5 $ liters $ = \dfrac{7}{2} $ liters
Now this volume of lemonade is served in $ \dfrac{1}{3} $ liter servings.
So, number of servings of $ \dfrac{1}{3} $ liter each \[ = \dfrac{{3.5}}{{\dfrac{1}{3}}} = \dfrac{{\left( {\dfrac{7}{2}} \right)}}{{\left( {\dfrac{1}{3}} \right)}}\]
Since the division of a fraction by another fraction is as good as multiplication of that same fraction by the inverse of the second fraction, we get,
 $ \Rightarrow $ Number of servings of $ \dfrac{1}{3} $ liter each $ = 3 \times 3.5 $
 $ \Rightarrow $ Number of servings of $ \dfrac{1}{3} $ each $ = 10.5 $
Now, the number of servings obtained when we mathematically interpreted the real time world problem is $ 10.5 $ servings. This can’t be practical as $ 10.5 $ servings make no sense in the real and practical world. Hence, we round off the number of servings of lemonade to the nearest integer possible so as to report an integer as the final answer.
But the number of lemonades is $ 10.5 $ and the decimal ends with a $ 5 $ at the tenths place. Hence, we can round off the number to both $ 10 $ as well as $ 11 $ . But it makes more sense to round off the $ 10.5 $ servings of lemonade to $ 10 $ servings as $ 10 $ servings are already available.
Thus total 10 servings of $ \dfrac{1}{3} $ liter each are made in the given quantity of the mixture.
So, the correct answer is “10 ”.

Note: We are given an algebraic word problem to be solved in this question. We can reframe and rewrite the mathematical word problem into an algebraic or arithmetic expression and solve accordingly with the help of algebraic and arithmetic rules.