Question

Als antifreeze makes three types of antifreeze Al's Special Blend which contains 54% ethylene glycol, Al's Deep Freeze which contains 72% ethylene glycol, and Al's Lite which contains 28% ethylene glycol. How many gallons of each antifreeze should Al mix to make 600 gallons of Al's Old Fashioned Antifreeze which is 44% ethylene glycol, if he is required to use twice as much of Al's Special Blend as of Al's Deep Freeze.

Answer 1

Emily, this is the solution:

• Special blend = 54% or 0.54 ethylene glycol (Twice as much as Deep freeze)

,

• Deep freeze = 72% or 0.72 ethylene glycol

,

• Lite = 28% or 0.28 ethylene glycol

We want 600 gallons of Old Fashioned Antifreeze 44% ethylene glycol

Let x to represent the number of gallons of Deep freeze, therefore:

0.72x + 0.54 (2x) = 600 (0.44)

0.72x + 1.08x = 264

1.8x = 264

Dividing by 1.8 at both sides:

1.8x/1.8 = 264/1.8

x = 146.7 (Gallons of Deep freeze)

2x = 293.4 (Gallons of Special blend)

Let's prove our answer is correct:

146.7 (0.72) + 293.4 (0.54) = 600 (0.44)

105.624 + 158.436 = 264

264 = 264

Our answer is correct. We need 146.7 Gallons of Deep freeze and 293.4 Gallons of Special blend.