An electronic pass for a toll road costs $30. The toll is normall...

Question

An electronic pass for a toll road costs $30. The toll is normally $5.00 but is reduced by 30% for people who have purchased the electronic pass. Determine the number of times the road must be used so that the total cost without the pass is the same as the total cost with the pass.

Accepted Answer

Hello. Today we're going to solve this word problem. So the problem states that the customer loyalty card in a coffee shop costs $24. A regular sized coffee typically cost $4. If a person presents a loyalty card, a discount of 20% will be applied identify the number of times that a person must buy a coffee so that the total price with and without the card is the same. So let's go ahead and figure out what the total price without the card is going to be. Well if you don't have the card, you're not paying the initial fee of $24 and instead you're paying $4 times the amount of cups that you're buying. So we can represent the total cost without the card as four times the cup of coffee which you can be represented with the variable X. Now if you're paying with the card, The total price is going to be the initial fee of the card which is $24 plus the discounted price of the coffee cup. Now again we are told that a 20% discount is applied to the coffee cups which is $4. So let's figure out what four minus 20% is going to be. Well 20% can be represented as 0. and 20% of $4 is going to be four times 0.2 which is equal to 0.8. So what we're gonna do is do 4 -0.8. And that's gonna give us 3.2, this is the discounted price For the coffee cups. So the total amount with the card is the initial fee, which is $24 plus $3.2 times the amount of coffee cups you buy, which is represented as X. Now, since we want to figure out how many coffee cups we need to buy for the price to be the same. We need to go ahead and equate both these equations together. In order to do that, we just set both of the price is equal to each other. So we get four X. Is equal to 24 plus 3. X. And now what we need to do is go ahead and sell for X. Well let's go ahead and get X to one side of the equation. And in order to do that, we're going to subtract 3.2 X from both sides of the equation. Doing so is going to give me 0.8 x equal to 24. And in order to solve for X, we need to divide both sides of this equation by 0.8, Dividing both sides of this equation by 0.8 is going to give us X. is equal to 30. So that means that you need to buy 30 coffee cups in order for both of the prices to be exactly the same. So this is going to be the solution to this word problem. And the answer to this problem is going to be be So I hope this video helps you understanding how to approach this type of word problem, and I'll go ahead and see you all in the next video.

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