I am cramming for an examine. I can not locate one of my graded lessons with all my notes. I am trying to redo the equaitons. I am really stuck on how to simplify this one.
Problem:
Studies indicate that the price elasticity of demand for cigarettes is about 0.4. If a pack of cigarettes currently costs $2 and the govenment wants to reduce smoking by 20 percent, by how much should the government increase the price?
The teacher wrote this out for the answer. I am not clear on how it is simplified to come down to the answer on 3.33
P2-2```2(P2-2)
_____= _______=0.5
(P2+2)``P2+2
2P2-4=0.5P2+1
1.5P2=5
P2=3.33
To simplify the equation and find the value of P2, you need to follow the steps written out by your teacher. Let's go through them one by one:
Step 1: Rewrite the equation using the given values:
(P2-2)/(P2+2) = 0.5
Step 2: Multiply both sides of the equation by (P2+2) to eliminate the denominator:
(P2-2) = 0.5 * (P2+2)
Step 3: Distribute 0.5 to both terms on the right side of the equation:
P2 - 2 = 0.5P2 + 1
Step 4: Simplify by combining like terms:
P2 - 0.5P2 = 1 + 2
Step 5: Combine the P2 terms:
0.5P2 = 3
Step 6: Divide both sides of the equation by 0.5 to isolate P2:
P2 = 3 / 0.5
Step 7: Simplify the division:
P2 = 6
So, it seems there is a mistake in the solution provided by your teacher. The correct answer should be P2 = 6, not 3.33. Double-check your notes and the equations you were given for any possible errors.