system of linear equations

Question

A chemical company makes two brands of antifreeze. The first brand is 55%

 pure antifreeze, and the second brand is 80%

 pure antifreeze. In order to obtain 130

 gallons of a mixture that contains 75%

 pure antifreeze, how many gallons of each brand of antifreeze must be used?

Answer 1

Let x = #gal @55%

y = #gal @80%

Then

x + y = 130 (because we want to end up with 130 gallons total)

Now let's look at the amount of antifreeze.

.55x + .8y = .75 (130) [antifreeze + antifreeze = antifreeze]

Let's multiply that last equation by 100 to eliminate decimals:

55 x + 80y = 75(130)

Let's use the substitution method, so solve 1st equation for x in terms of y:

x = 130 - y.

After substitution into the antifreeze equation we have:

55 (130 - y) + 80y = 75(130)

55(130) - 55y + 80y = 75(130)

25y + 55(130) = 75(130)

25y = 75(130) - 55(130)

25y = 20(130)

y = 20(130)/25 = 520/5 = 104 gallons of 80% antifreeze

x = 130 - 104 = 26 gallons of 55% antifreeze

Check the antifreeze:

.55(26) + .8(104) =? .75(130)

14.3 + 83.2 =? 97.5

97.5 = 97.5 check