Question

How many gallons of $4\% $ milk should you mix with $1\% $ milk to make $10$ gallons of $3\% $ milk?

Answer 1

Hint: Identify the known and unknown ratios and set up the ratio and proportion and solve accordingly. In these ratio and proportion types of questions, take any variable as the reference number where applicable.

Complete step by step answer:
Let us assume that “x” gallons of $4\% $milk is mixed with the $(10 - x)$gallons of $1\% $ milk to make $10$gallons of $3\% $ milk.
Now, equating the milk content –
We get –
$x(0.04) + (10 - x)(0.01) = 10(0.03)$
Now, Multiple both the sides of the above equation with
$ \Rightarrow 4x + 10 - x = 30$
Make like terms together, when you move any term from one side of the equation to the opposite side of the equation, the sign of the terms also changes.
$ \Rightarrow 4x - x = 30 - 10$
Simplify the above equation –
$ \Rightarrow 3x = 20$
Term multiplicative on one side if moved to the opposite side, then it goes to the denominator.
$ \Rightarrow x = \dfrac{{20}}{3}$
Convert it in the form of mixed fraction.
$ \Rightarrow x = 6\dfrac{2}{3}$
and
$
  (10 - x) = 10 - \dfrac{{20}}{3} \\
  10 - x = 3\dfrac{1}{3} \\
 $
Hence, $6\dfrac{2}{3}$gallons of $4\% $ milk is mixed with $3\dfrac{1}{3}$ gallons of $1\% $milk to prepare $10$ gallons of $3\% $ of milk.

Note: Always read the question twice and frame the word statement in the mathematical form. Segregate all the known and unknown terms and form the corresponding ratios and the proportions accordingly. Be careful about the sign while doing simplification and remember the golden rules-
Addition of two positive terms gives the positive term
Addition of one negative and positive term, you have to do subtraction and give signs of bigger numbers, whether positive or negative.
Addition of two negative numbers gives a negative number but in actual you have to add both the numbers and give a negative sign to the resultant answer.