Answer:
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.
Answer: 37.5 liters
Step-by-step explanation:
Note: Create a table. Multiply across and add down. The bottom row creates the equation.
[tex]\begin{array}{l|c|c|l}&\underline{\quad Qty \quad}&\underline{\qquad \% \qquad}&\underline{\qquad Qty \times \% \qquad}\\Solution\ A&x&32\%=0.32&x(0.32)=0.32x\\\underline{Solution\ B}&\underline{\quad 15\quad}&\underline{81\% =0.81}&\underline{15(0.81)=12.15\quad}\\Mixture&x+15&46\% =0.46&\quad 0.32x+12.15\\\end{array}\\[/tex]
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
