Assume that S/A = 5.2, D/A = .40, N/E = .75 and A = D + E. Solve for N/S.
A=D+E
S/5.2=.4A + N/.75
S/5.2=.4*S/5.2 + N/.75
S(1/5.2-.4/5.2)=N/.75
N/S= .75(1/5.2-.4/5.2)
D = 0.40A
A = D+E = 0.40A+E so E = 0.60A
N = 0.75E = 0.45A
S = 5.2A
N/S = 0.45/5.2 = 45/520
To solve for N/S, we need to use the given information and mathematical equations.
First, let's write down the information and equations given:
S/A = 5.2 (Equation 1)
D/A = 0.40 (Equation 2)
N/E = 0.75 (Equation 3)
A = D + E (Equation 4)
To solve for N/S, we need to eliminate the variables D and E from the equations.
From Equation 2, we can isolate D by multiplying both sides by A:
D = 0.40 * A (Equation 5)
Substitute Equation 5 into Equation 4 to eliminate D:
A = (0.40 * A) + E
Now, let's substitute the value of A from Equation 4 into Equation 1:
S/(0.40 * A) = 5.2
Next, multiply both sides by (0.40 * A) to isolate S:
S = 5.2 * (0.40 * A)
Simplify further:
S = (5.2 * 0.40) * A
S = 2.08 * A (Equation 6)
Now, substitute the value of A from Equation 5 into Equation 6:
S = 2.08 * (0.40 * A)
Multiply all the constants:
S = 0.832 * A
Rearrange Equation 3 to solve for E:
E = (N / 0.75)
Now substitute the value of E in Equation 4:
A = D + (N / 0.75)
Now, substitute the value of D from Equation 5:
A = (0.40 * A) + (N / 0.75)
Multiply both sides by 0.75 to eliminate the fraction:
0.75 * A = (0.40 * A) + N
Now, subtract (0.40 * A) from both sides:
0.75 * A - 0.40 * A = N
Simplify the left side:
0.35 * A = N
Divide both sides by A:
0.35 = N / A
Now substitute the value of A from Equation 6:
0.35 = N / (0.832 * A)
Multiply both sides by (0.832 * A) to isolate N:
N = 0.35 * (0.832 * A)
Simplify further:
N = 0.2912 * A
Finally, substitute the value of A from Equation 5:
N = 0.2912 * (0.40 * A)
Multiply all the constants:
N = 0.11648 * A
So, N/S = N / 2.08 * A. Substitute the value of N from the last equation:
N/S = (0.11648 * A) / (2.08 * A)
Now, cancel out A from the numerator and denominator:
N/S = 0.11648 / 2.08
Divide and simplify:
N/S = 0.056