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GrogVix [38]
3 years ago
11

A chemical company makes two brands of antifreeze. The first brand is 20% pure antifreeze, and the second brand is 70% pure anti

freeze. In order to obtain 30 gallons of a mixture that contains 35% pure antifreeze, how many gallons of each brand of antifreeze must be used?
Mathematics
1 answer:
andre [41]3 years ago
3 0

Answer:

First brand of antifreeze: 21 gallons

Second brand of antifreeze: 9 gallons

Step-by-step explanation:

Let's call A the amount of  first brand of antifreeze. 20% pure antifreeze

Let's call B the amount of second brand of antifreeze. 70% pure antifreeze

The resulting mixture should have 35% pure antifreeze, and 30 gallons.

Then we know that the total amount of mixture will be:

A + B = 30

Then the total amount of pure antifreeze in the mixture will be:

0.2A + 0.7B = 0.35 * 30

0.2A + 0.7B = 10.5

Then we have two equations and two unknowns so we solve the system of equations. Multiply the first equation by -0.7 and add it to the second equation:

-0.7A -0.7B = -0.7*30

-0.7A -0.7B = -21

-0.7A -0.7B = -21

               +

0.2A + 0.7B = 10.5

--------------------------------------

-0.5A = -10.5

A = \frac{-10.5}{-0.5}

A = 21\ gallons

We substitute the value of A into one of the two equations and solve for B.

21 + B = 30

B = 9\ gallons

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\implies {\blue {\boxed {\boxed {\purple {\sf {Your\:answer\:is\:59.}}}}}}

\sf \bf {\boxed {\mathbb {Step-by-step\:explanation:}}}

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