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✓g✓ 10✓ 11✓ 12✓ 13141516✓ 1718✓ 1920A chemical company makes two brands of antifreeze. The first brand is 20% pure antifreeze, and the second brand is 70% pure antifreeze. In order to obtain90 gallons of a mixture that contains 60% pure antifreeze, how many gallons of each brand of antifreeze must be used?OoFirst brand:Il gallons52Second brand:gallonsSave For LaterSubmit AssignmentCheck© 2021 McGrawki Education. All Rights Reserved. Terms of Use Privacy Acces1039 PM

Sagot :

Problem:

A chemical company makes two brands of antifreeze the first brand is 20% pure antifreeze and the second brand is 70% pure antifreeze in order to obtain 90 gallons of a mixture that contains 60% pure antifreeze how many gallons of each brand of antifreeze must be used.

Solution:

Let x = amount of 20% pure antifreeze.

Let y = amount of 70% pure antifreeze.

Then, we have the following equations:

Equation 1:

x+y = 90 gallons (total of 90 gallons mixed)

Equation 2:

(0.20)x+(0.70)y = 0.60(x+y)

that is:

0.60x - 0.20x = 0.70y -0.60 y

that is :

0.40x = 0.10 y

Simplify and solve the system of equations. From equation 1, solve for x:

[tex]x\text{ = }90-y[/tex]

replace this in equation 2:

[tex]0.40(90-y)\text{ = 0.10y}[/tex]

that is:

[tex]36-0.40y\text{ = 0.10y}[/tex]

that is:

[tex]36\text{= 0.10y}+\text{ 0.40y = 0.50y}[/tex]

solve for y:

[tex]y\text{ = }\frac{36}{0.50}\text{ = 72 gallons }[/tex]

then we can conclude that we need 72 gallons of the brand with an amount of 70% pure antifreeze. Now, replace this value in equation 1, and solve for x :

[tex]x\text{ = }90-72\text{ = 18 gallons }[/tex]

then we can conclude that we need 18 gallons of the brand with an amount of 20% pure antifreeze.

Then the solution is:

- we need 18 gallons of the brand with an amount of 20% pure antifreeze.

-we need 72 gallons of the brand with an amount of 70% pure antifreeze.

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