0.8p - 50 < = 150
0.8p < = 150 + 50
0.8p < = 200
p < = 200/0.8
p < = 250
the reason I set it up this way is because when it is 20% off, u r actually paying 80% of the original price (p)....80% of the original price is written as 0.8p...then u subtract ur 50 dollar discount coupon...- 50.....and if all she can spend is 150....it would be less then or equal to 150. So the most she can spend on the phone is 250
I don't really know if this is correct but I think it is x+y+z=14
Answer:
x = 50*e∧ -t/100
Step-by-step explanation:
We assume:
1.-That the volume of mixing is always constant 300 gallons
2.-The mixing is instantaneous
Δ(x)t = Amount in - Amount out
Amount = rate * concentration*Δt
Amount in = 3 gallons/ min * 0 = 0
Amount out = 3 gallons/min * x/ 300*Δt
Then
Δ(x)t/Δt = - 3*x/300 Δt⇒0 lim Δ(x)t/Δt = dx/dt
dx/dt = - x/100
dx/ x = - dt/100
A linear first degree differential equation
∫ dx/x = ∫ - dt/100
Ln x = - t/100 + C
initial conditions to determine C
t= 0 x = 50 pounds
Ln (50) = 0/100 * C
C = ln (50)
Then final solution is:
Ln x = - t/100 + Ln(50) or
e∧ Lnx = e ∧ ( -t/100 + Ln(50))
x = e∧ ( -t/100) * e∧Ln(50)
x = e∧ ( -t/100) * 50
x = 50*e∧ -t/100
