A chemical company makes two brands of antifreeze. The first brand is 70% pure antifreeze, and the second brand is 95% pure antifreeze. In order to obtain 180 gallons of a mixture that contains 90% pure antifreeze, how many gallons of each brand of antifreeze must be used?

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Mathematics

Nickolas Fuller

31 May, 10:08

A chemical company makes two brands of antifreeze. The first brand is 70% pure antifreeze, and the second brand is 95% pure antifreeze. In order to obtain 180 gallons of a mixture that contains 90% pure antifreeze, how many gallons of each brand of antifreeze must be used?

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Cara Avila · Answer 1

Let a be the amount needed of 70% pure antifreeze, and let b be the amount needed of 95% pure antifreeze.

0.7a + 0.95b = 180 * 0.9 ... (1)

a + b = 180 ... (2)

b = 180 - a ... (3)

Plugging the expression for b in equation (3) into equation (1), we get:

0.7a + 0.95 (180 - a) = 162 ... (4)

Solving equation (4) gives the value a = 36, and plugging this value for a into equation (2) we get b = 144.

Amounts needed are therefore 36 gallons of 70% pure antifreeze and 144 gallons of 95% pure antifreeze.