The cost of an air conditioner is b dollars more than 3 times the cost

Let the cost of a radio be $100. Let the value of ‘b’ be $50. Then,

Cost of an air-conditioner = 3* 100 + 50 = $350.

The total cost of an air-conditioner and a radio, v = 350 + 100 = $450

Now, the only thing left is to figure out is which option will give us 350 when we substitute the respective values of the variables.

Option A is \(\frac{(v-b) }{ 4}\) = \(\frac{(450 – 50) }{ 4}\) = 100, which is the cost of the radio and not the air-conditioner. Option A can be eliminated.

Option B can be eliminated since \(\frac{(v-b) }{ 3}\) gives us \(\frac{400}{3}\), which doesn’t represent the cost of anything in this situation.

I’m assuming that the 2y in option C is actually 2v (there’s no variable y mentioned in the question). sajjad Ahmad, please clarify.

\(\frac{(2v+b) }{ 3}\) = \(\frac{950 }{ 3}\), which is not the cost of the air conditioner. Option C can also be eliminated.

\(\frac{(v+3b) }{ 4}\) = \(\frac{600 }{ 4}\) which is not the cost of the air conditioner. Option D can be eliminated.

The only option left is E, that has to be the right answer. \(\frac{(3v + b) }{ 4}\) = \(\frac{(1350 + 50) }{ 4}\) = \(\frac{1400 }{ 4}\) = 350 which is definitely the price of the air conditioner.

Answer option E is the correct answer.

When there are variables in the options and the question, plug in simple values and use those values to evaluate options and eliminate the wrong answers. Of course, you can also develop expressions and solve the question, but sometimes this may require more time and effort. Dealing with numbers is always easier.

Hope that helps!