SOLUTION: An engine has a 4.6 litre capacity cooling system. If the most ideal solution of antifreeze for this engine is a 55.1 % solution (a mix of 55.1 % pure antifreeze and 44.9 % water).

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Question 1135345: An engine has a 4.6 litre capacity cooling system. If the most ideal solution of antifreeze for this engine is a 55.1 % solution (a mix of 55.1 % pure antifreeze and 44.9 % water). How much pure antifreeze (in litres) must be combined with a 45.4 % solution to achieve 4.6 litres of the ideal solution?
Express your answer to three significant digits.
Found 3 solutions by greenestamps, josgarithmetic, ikleyn:
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!

Using the traditional algebraic method for solving the problem, write an equation that says x liters of pure (100%) antifreeze must be added to (4.6-x) liters of 45.4% antifreeze to get 4.6 liters of 55.1% antifreeze:

<--- corrected equation, thanks tutor @ikleyn; I previously showed .0454 and .0551....

Ugly numbers; I'll let you finish the solution by that method.

Here is a MUCH easier way to get the answer to a problem like this, based on the concept that the ratio in which the two ingredients need to be mixed is directly related to where the target percentage of 55.1% lies between the 45.4% and 100% percentages of the ingredients.

Here without detailed explanation are the required calculations for your problem.

(1) 55.1-45.4 = 9.7; 100-45.4 = 54.6
(2) 9.7/54.6 = 0.177655678... is the fraction of the way that 55.1% is from 45.4% to 100%, so it is the fraction of the mixture that needs to be the higher percentage ingredient
(3) 0.177688678*4.6 = 0.817216... is the number of liters of pure antifreeze that must be used in the mixture.

ANSWER (to 3 significant digits): 0.817 liters

Answer by josgarithmetic(39617)   (Show Source):
You can put this solution on YOUR website!
M=4.6, volume capacity to meet, in litres
T=55.1, percent concentration for most ideal solution
H=100, percent pure antifreeze
L=45.4, percent of available lower conc. antifreeze
x, unknown volume of pure 100% antifreeze to use
M-x, unknown volume of L % antifreeze to use

Solve that equation for x.
.
.
.

Answer by ikleyn(52787)   (Show Source):
You can put this solution on YOUR website!
.

            Unfortunately, in the post by @greenestamps the base equation is written with a mistake,

            so I came to fix it and to provide correct algebraic solution.

Let x be the amount (the volume) of the pure antifreeze to mix (precisely the value under the problem's question). Then your base equation is x + 0.454(4.6-x) = 0.551*4.6 saying that the amount of the pure antifreeze in the mixture is the sum of its amounts in the ingredients. Notice that this equation is different from that of the post by @greenstamps, where it was written with mistake. The solution is in one line x = = (one click in Excel in my computer) = 0.817 liters. ANSWER

Solved.

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There is entire bunch of 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 dry substances like coffee beans, nuts, cashew and peanuts
    - Word problems on mixtures for dry substances like candies, dried fruits
    - Word problems on mixtures for dry substances like soil and sand
    - Word problems on mixtures for alloys
    - Typical word problems on mixtures from the archive
    - Advanced mixture problems
    - Advanced mixture problem for three alloys
    - OVERVIEW of lessons on word problems for mixtures
in this site.

A convenient place to quickly observe these lessons from a "bird flight height" (a top view) is the last lesson in the list.

Read them and become an expert in solution the 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 online textbook 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.