Question

Sally Finkelstein has a recipe that calls for horseradish sauce that is 60​% pure horseradish. At the grocery store she finds one horseradish sauce that is 20​% pure horseradish and another that is 70​% pure horseradish. How many teaspoons of each of these horseradish sauces should Sally mix together to get 4 teaspoons of horseradish sauce that is 60​% pure​ horseradish?

Answer 1

0.8 spoons of 20​% pure horseradish and 3.2 spoons of 70 % pure horse radish is mixed to get 4 table spoons of 60 % pure horse radish

Solution:

Each of these horseradish sauces should Sally mix together to get 4 teaspoons of horseradish sauce that is 60​% pure​ horseradish

Let x be the number of spoons of 20 % pure horse radish

Then (4 - x)  be the number of spoons of 70 % pure horse radish

Therefore,

x spoons of 20​% pure horseradish and (4 - x) spoons of 70 % pure horse radish is mixed to get 4 table spoons of 60 % pure horse radish

Therefore, we can frame a equation as:

20 % of x + 70 % of (4-x) = 60 % of 4

$\rightarrow 20 \% \times x + 70 \% \times (4 - x) = 60 \% \times 4\\\\\rightarrow \frac{20}{100} \times x + \frac{70}{100} \times 4-x = \frac{60}{100} \times 4\\\\\rightarrow 0.2x+0.7(4-x)=0.6 \times 4\\\\\rightarrow 0.2x+2.8-0.7x=2.4\\\\\rightarrow -0.5x=2.4-2.8\\\\\rightarrow -0.5x=-0.4\\\\\rightarrow x = 0.8$

Thus 0.8 spoons of 20 % pure horse radish is used

Then, 4 - x = 4 - 0.8 = 3.2

Thus 3.2 spoons of 70 % pure horse radish is used