SOLUTION: You need to prepare a 47 mL of a 24% syrup/soda �prescription�. To do this, you can use the 80% syrup solution and the 10% soda solution that you have in stock. How many mL of each

Question 1110986: You need to prepare a 47 mL of a 24% syrup/soda �prescription�. To do this, you can use the 80% syrup solution and the 10% soda solution that you have in stock. How many mL of each solution do you need to create this final solution?
Found 3 solutions by ikleyn, mananth, greenestamps:
Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.

Let x = the amount (in mL) of the 80% syrup solution. Then your equation to find x is THIS = 0.24 saying that the fraction in the left side is exactly the required amount of the sirup to provide 24% concentration 47 mL solution. To solve the equation, multiply both sides by 47 to get 0.8x + 4.7 - 0.1x = 0.24*47, 0.7x = 0.24*47 - 4.7 = 6.58, x = = 9.4. Answer. 9.4 mL of the 80% sirup solution and 47-9.4 = 37.6 mL of the 10% sirup solution. Check. = 0.24 = 24%. ! Correct !

Solved.

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It is a typical mixture solution word problem.

There is entire bunch of introductory lessons covering various types of mixture problems
    - Mixture problems
    - More Mixture problems
    - Solving typical word problems on mixtures for solutions
    - Word problems on mixtures for antifreeze solutions
    - Word problems on mixtures for alloys
    - Typical word problems on mixtures from the archive
    - Advanced mixture problems
    - Advanced mixture problem for three alloys
in this site.

You will find there ALL TYPICAL mixture problems with different methods of solutions,
explained at different levels of detalization, from very detailed to very short.

Read them and become an expert in solution mixture word problems.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook in the section "Word problems" under the topic "Mixture problems".

Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.

Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!
component percentage ----------------quantity
Syrup 80 ---------------- x Oz
soda 10 ---------------- 47 - x Oz
Mixture 24.00% ---------------- 47

80 x + 10 ( 47 - x ) = 24.00 * 47

80 x + 470 - 10 x = 1128
80 x - 10 x = 1128 - 470
70 x = 658
/ 70
x = 9.4 Oz 80.00% syrup
37.6 Oz 10.00% soda

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

Here are three versions of a method for solving mixture problems involving two ingredients that is very different from the standard solution method used by both of the other tutors who have responded to your question. This method is based on the fact that the ratio in which the two ingredients are mixed exactly determines the percentage of the mixture.

In your example, you are mixing 10% syrup solution and 80% syrup solution to get a 24% syrup mixture.

Of the three version described below, two are different ways of thinking of the problem; the third uses a kind of chart that does basically the same calculations in a different way. But all three are basically using the same idea of the ratio in which the two ingredients need to be mixed.

(1) One way to think of the given information is this: The 24% is "4 times as close" to 10% as it is to 80%: 24-10 = 14; 80-24 = 56; 14*4 = 56. That "4 times as close" means you need to use 4 times as much of the 10% ingredient as the 80% ingredient.

(2) Another way to think of the given information is this: The 24% is 1/5 of the way from 10% to 80% (24-10 = 14; 80-10 = 70; 14/70 = 1/5). The "1/5 of the way from 10%" means only 1/5 of the mixture must be the other (80%) ingredient, leaving 4/5 of the mixture to be the 10% ingredient.

(3) And here is a way to put the given information in a table to get the answer.

In this table, the numbers in the first column are the percentages of the two ingredients and the number in the second column is the percentage of the mixture. The numbers in the third column are the differences, calculated diagonally, between the numbers in the first and second columns: 80-24=56; 24-10=14.

When the calculations are done this way, the numbers in the third column show the ratio in which the two ingredients must be mixed -- in this problem, 14:56, or 1:4.

So each of these three versions, with only a few simple calculations, shows us that the ratio of the amounts of the two ingredients must be 4:1, or that the mixture must be made up of 1/5 of one ingredient and 4/5 of the other.

In this problem, where we need 47ml of the mixture, the amount of the 80% syrup required is 1/5 of 47ml or 9.4ml; the amount of the 10% syrup required is 4/5 of 47ml, or 37.6ml.
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