Question

9) Wilbur wants to make 7.6 gal. of a 35%

alcohol solution by mixing together a 80%
alcohol solution and a 20% alcohol solution.
How much of each solution must he use?

Answer 1

1.9 gallons of the 80% solution.

5.7 gallons of the 20% solution,

Explanation:

Let the volumes of the 80% and 20 % solutions be x and y gallons.

Then:

x + y = 7.6.

Also, using amounts of pure alcohol:

0.8x + 0.2y = 7.6 * 0.35

0.8x + 0.2y = 2.66 Multiplying this equation by -5:

-4x - y = - 13.3 Adding this to the first equation:

-3x = -5.7

= 1.9 gallons.

y = 7.6 - 1.9

= 5.7 gallons.

Answer 2

1.9 gallons of 80% and 5.7 gallons of 20%

Explanation:

x gallons of 80% alcohol solution is mixed with y gallons of 20% alcohol to make 7.6 gallons of 35% alcohol solution.

Based on the given, we get two equations:

• x+y = 7.6
• 0.8x + 0.2y = 7.6*0.35= 2.66

Let's substitute y with y = 7.6 - x:

• 0.8x + 0.2(7.6 - x) = 2.66
• 0.8x + 1.52 - 0.2x = 2.66
• 0.6x = 2.66 - 1.52
• 0.6x = 1.14
• x= 1.14/0.6
• x= 1.9 gal.

Then we find the value of y:

• y = 7.6 -x
• y = 7.6 - 1.9
• y = 5.7 gal.

So the answer is:

• 1.9 gallons of 80% and 5.7 gallons of 20% solutions mixed