Question

Amounts of a 35% alcohol solution and a 65% alcohol solution are to be mixed to produce
24 gallons of a 45% alcohol solution. How many gallons of the 35% alcohol solution and
how many gallons of the 65% alcohol solution should be used?

Answer 1

Step-by-step explanation:

Amount of alcohol in 12 gallons mix is 12*0.4=4.8gallons

Let 50%alcohol in x gallons

so alcohol in in x gallons is 0.5x

Balance mix =12-x gallons

Alcohol in balance mix =0.35(12-x)

4.8=0.5x+4.2–0.35x

0.6=0.15x

x=4 gallons

So 50% alcohol of 4 gallons and 35% alcohol of 8 gallons are to be mixed to get 40% of alcohol in 12 gallons

Answer 2

$\large\underline{\sf{Solution-}}$

Let assume that

• Amount of 35 % alcohol solution used be x gallons

• Amount of 65 % alcohol solution used be y gallons

So,

According to statement,

Total solution obtained is 24 gallons.

$\rm :\longmapsto\:x + y = 24$

$\bf :\longmapsto\:x = 24 - y - - - (1)$

Now,

According to statement again,

Amounts of a 35% alcohol solution and a 65% alcohol solution are to be mixed to produce 24 gallons of a 45% alcohol solution.

$\rm :\longmapsto\:\dfrac{35}{100} x + \dfrac{65}{100} y = \dfrac{45}{100} (x + y)$

$\rm :\longmapsto\:35x + 65y = 45(x + y)$

$\rm :\longmapsto\:35x + 65y = 45x + 45y$

$\rm :\longmapsto\: 65y - 45y= 45x - 35x$

$\rm :\longmapsto\:20y= 10x$

$\rm :\longmapsto\:2y= x$

$\rm :\longmapsto\:2y= 24 - y \: \: \: \: \: \: \: \: \{ \: using \: (1) \: \}$

$\rm :\longmapsto\:3y = 24$

$\bf\implies \:y = 8$

On substituting the value of y in equation (1), we get

$\bf :\longmapsto\:x = 24 - 8 = 16$

Thus,

Amount of 35 % alcohol solution used be 16 gallons

Amount of 65 % alcohol solution used be 8 gallons