How many liters of a 32 % alcohol solution must be mixed with 15 liters of a 81% alcohol solution to get a 46% alcohol in the entire solution?

37.5 liters of 32% solution

Step-by-step explanation:

Assign variables

let "a" be the number of liters to add from the 32% alcohol solution

let "c" be the number of liters to have a 46% alcohol solution

Create equations using the information given in the problem.

Equation for total liters

a + 15 = c

Equation for percentage

0.32a + 0.81(15) = 0.46c

0.32a + 12.15 = 0.46c

Substitute the expression for total liters into the equation for percentage. Both equations have "c".

0.32a + 12.15 = 0.46c                   Equation for percentage

0.32a + 12.15 = 0.46(a + 15)                 Substituted expression

0.32a + 12.15 = 0.46a + 6.9

Start isolating "a"

0.32a + 12.15 - 12.15 = 0.46a + 6.9 - 12.15     Subtract 12.15 on both sides

0.32a = 0.46a - 5.25

0.32a - 0.46a = 0.46a - 0.46a - 5.25             Subtract 0.46a on both sides

-0.14a = -5.25

-0.14a/-0.14 = -5.25/-0.14                    Divide both sides by -0.14

a = 37.5                      Liters to add from 32% alcohol solution

If you need to know how many liters your final solution is:

Substitute a = 37.5 into the equation for total liters

a + 15 = c  

37.5 + 15 = c                     Add

c = 52.5                 Liters of final solution

Check your answer using the equation for percentage

0.32a + 0.81(15) = 0.46c             Substitute a=37.5 and c=52.5

0.32(37.5) + 0.81(15) = 0.46(52.5)              Multiply each term

12 + 12.15 = 24.15               Add to simplify

24.15 = 24.15            Same answer

LS = RS                   Left side equals right side

Therefore 37.5 liters of the 32% alcohol solution must be added with 15 liters of an 81% alcohol solution.

 37.5 liters

Step-by-step explanation:

Note: Create a table. Multiply across and add down. The bottom row creates the equation.

                                   0.46(x + 15) = 0.32x + 12.15

                                   0.46x + 6.9 = 0.32x + 12.15

                                   0.14x  + 6.9 =              12.15

                                   0.14x           =               5.25

                                          x           =               37.5

step-by-step explanation:

6.48/4 4 goes into 6.48 1.62 times

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b