Question

A bridge has been constructed between the mainland and

anisland. The total cost (excluding toll) to travel across
thebridge is expressed as C=50+0.5V, where V is the number of
veh/dayand C is the cost/vehicle in cents. The demand for
travelacross the bridge is V=2500-10C.
(a)Determine the volume of traffic across the bridge.
(b)If a toll of 25 cents is added, what is the volume
acrossthe bridge?

Answer 1

a) 333,33 b)291,67

Step-by-step explanation:

you have both equations :

C=50+0.5V and V=2500-10C

and you want to know the variable V so, you can calculate V in function of C, and you have already clear the variable "C", then you replace for (a):

1. V=2500-10C
2. V=2500-10(50+0.5V)
3. V=2500-500-5V
4. V+5V=2500-500
5. 6V=2000
6. V=2000/6
7. V=333,33

for b) they tell you that you increase your constant of the equiation C=50+0.5V (remember that the constant is the one alone, wihout any variable, in this case "50") increase in 25 so, your equiation for this point of C is C=75+0.5V, then you do the same:

1. V=2500-10C
2. V=2500-10(75+0.5V)
3. V=2500-750-5V
4. V+5V=2500-750
5. 6V=1750
6. V=1750/6
7. V=291,67

It's a system of two equations and two variables, wich gives you a compatible define system, it gives you only one solution.

I hope it helps you.