i need to know how to work this problem out and the answer.

Question

the cafe is preparing lemonade for lunch. too many people are in the mixing process and the mix is too sweet. How many quarts of water must be added to 40 quarts of lemonade that is 50% sugar to make lemonade that is 30% sugar. Round the number of quarts needed to the nearest whole quart.

Answer 1

With mixture problems, it is a good rule of thumb to find the pure substance. In this case, it is the sugar. If we have 40 quarts of 50% sugar lemonade. That means, there is 20 quarts of just sugar in this lemonade. The same amount of sugar remains, we will be adding water to dilute and the result must be 30%.

 

The equation is: 

 

3/10 = 20/x 

 

cross multiply, the result: 

 

(20)10 = 3x 

 

200 = 3x 

 

66.6 quarts make a 30% solution of lemonade with 20 quarts of sugar. Thus, you must add 27 more quarts of water to the existing solution.