Search 72,997 tutors
0 0

A solution of 68% alcohol is to be mixed with a solution of 22% alcohol to form 460 liters of a 61% solution. How many liters of the 68% solution must be used?

would it be A. 413 Liters   B. 380 liters   c. 390 liters  D. 166 liters

Since the answer section doesn't seem to want to take my update, here it is:

Let's call the quantity of 68% alcohol x and the quantity of 22% alcohol y.

We know that x + y = 460 liters

Now we have to consider the concentrations of the solutions. We do this by taking the concentration and multiplying by the volume:

.68 (x) + .22 (y) = .61 (460)

From the first equation, we can solve for y: y = 460 - x
and replace that in for y in the second equation:
.68(x) + .22 (460 - x) = .61 (460)

Simplify and combine like terms:

.68x + 101.2 - .22x = 280.6

.46x = 179.4

x = 390 liters

Let x = amount (liters) of 68% solution

then

460-x = amount (liters) of 22% solution

.68x + .22(460-x) = .61(460)

.68x + 101.2-.22x = 280.6

.68x - .22x = 179.4

.46x = 179.4

x = 390 liters

Say A liters of 68% alcohol solution must be used.

So it will have a total alcohol contents of Ax68/100=68xA/100 liters

Therefore (460-A) liters of 22% alcohol is used with total alcohol contents of (460-A)x22/100 liters

Total alcohol contents in 460 liter of 68% alcohol solution is

68xA/100+22x(460-A)/100=(68A+22x460-22A)/100=(46A+10120)/100 liters....(1)

61% alcohol content in 460 liters = 460x61/100 liters of alcohol....(2)

Since alcohol contents from equation (1) and (2) must equal

460x61/100 = (46A+10120)/100

28060/100=(46A+10120)/100.....multiply both sides by 100

100x28060/100=100x(46A+10120)/100

28060=46A+10120

28060-10120=46A

17940=46A...divide both sides by 46

A=17940/46=390

So 390 liters of 68% solution must be used.

Let's call the quantity of 68% solution x and the quantity of 22% solution y.

We know that x + y = 460 liters

Now we have to consider the concentrations of the solutions. We do this by taking the concentration and multiplying by the volume:

.68 (x) + .22 (y) = .61 (460)

From the first equation, we can solve for y: y = 460 - x
and replace that in for y in the second equation:
.68(x) + .22 (460 - x) = .61 (460)

Simplify and combine like terms:

.68x + 101.2 - .22x = 280.6

.46x = 179.4

x = 390 liters