Use c1v1+c2v2=c3v3
where c=concentration, v=volume.
C1=0.12
V1=20 L
C2=0.36
V2=X
C3=0.20
V3=20+X L
Substitute in equation
0.12(20) + 0.36X = 0.20(20+X)
Expand
2.4 + 0.36X = 4 + 0.2X
Simplify
(0.36-0.2)X = 4-2.4
0.16X = 1.6
X=1.6/0.16 = 10 L
check:
0.12(20)+0.36(10)=2.4+3.6=6.0
(20+10)*0.20 = 6.0 so solution is good.
Answer: Volume of 36% solution is 10L
This problem can be solved by algebraic method.
Let
x = the total time spent of all clients in Plan A
y = the total time spent of all clients in Plan B
We represent two variables x and y because there are two plans that won't be happened simultaneously.
On Wednesday, the two workout plans have the total time of 6 hours. We equate
3x + 5y = 6
While on Thursday, the total time is 12 hours. We also equate
9x + 7y = 12
To find x and y, we can use the substitution method. For the first equation, we arrange it in terms of y, that is
5y = 6 - 3x
y = (6 - 3x)/5
Substitute it to the second equation:
9x + (7/5)(6 - 3x) = 12
9x + (42/5) - (21/5)x = 12
Multiply the equation by 5 to cancel the denominator:
45x + 42 - 21x = 60
45x - 21x = 60 - 42
24x = 18
x = 18/24 = 3/4 hours
For y:
3(3/4) + 5y = 6
9/4 + 5y = 6
Multiply the equation by 4 to cancel the denominator:
9 + 20y = 24
20y = 24 - 9
20y = 15
y = 15/20 = 3/4 hours
Hence, each workout plans are done within 3/4 hours (or 45 minutes).
We know |x| ≥ 0 for all real numbers. Therefore your answer is x ∈ ∅ (no solution).
Answer: The answer would be $50. Hope this helps :)
Step-by-step explanation:
