Three companies are selling theatre tickets. The normal price for ticket is the same in each company. But each company is currently running a deal. Company A is selling two tickets at full price and then selling the third for half price. Company B is selling all tickets for 20 percent off their full price. Company C is selling three tickets at full price and then giving away the fourth for free. Sally wants to buy six tickets. Which company should she buy from to ensure she gets the cheapest price?
Well, first of all, I’m gonna call the full price 𝑃. And I can do that because we know that the normal full price of a ticket is the same in each company. So then, what I’m gonna do now is work out how much the cost will be for each company in turn. And I’m gonna start with company A.
Well, company A is selling two tickets at full price and then selling the third for half price. So therefore, if we’re using company A to buy three tickets, the cost would be two 𝑃 because there’s two full price tickets plus a half 𝑃 because the third is half price.
However, we want to buy six tickets. So it’s going to be two lots of two 𝑃 plus a half 𝑃. So we can write that as two 𝑃 plus a half 𝑃 plus two 𝑃 plus a half 𝑃 which is gonna give us five 𝑃 because you got two 𝑃 plus two 𝑃 which is four 𝑃. And then, we’ve got two lots of a half 𝑃. So we can say that two multiplied by a half 𝑃 just gives us 𝑃, so added together to give us five 𝑃.
Okay, so now, let’s look at company B. Well, company B is selling all the tickets for 20 percent off their full price. So therefore, to calculate the cost for six tickets, it’s gonna be six 𝑃, so six full price tickets, multiplied by 0.8. And the reason it’s multiplied by 0.8 is because if you had the full price for a ticket, it would be 100 percent. And then, in the offer, the taken 20 percent off, well 100 minus 20 is gonna give us 80. So that’s 80 percent.
Well, 80 percent is 80 out of 100 or 80 over 100 because percent means out of 100 which is the same as eight cents. So this is equal to 0.8. So our multiplier will be 0.8. Okay, so we’ve got six 𝑃 multiplied by 0.8 which is gonna give us an answer of 4.8𝑃. And the way I did is because I did six multiplied by eight which is 48. But then in the original calculation, so six 𝑃 multiplied by 0.8, we can see that there’s one number after the decimal point. So therefore, we’ve got one decimal place. So we put that back into our answer. So we get 4.8.
So then, we can take a look at company C. And company C is selling three tickets at full price and then giving away the fourth for free. So if we think about how this is gonna work if we want to buy six tickets, they will buy three tickets at full price, so that’s one, two, three. Then, we get the fourth one for free. So I’ll put that here as a zero. And then, we’d have to buy the final two tickets at full price.
So we got 𝑃 plus 𝑃 plus 𝑃 plus zero plus 𝑃 plus 𝑃 which is gonna give us the answer of five 𝑃 because we’ve had to buy five of the tickets at full price and we’ve got one free.
So now, what we’ve done is we’ve calculated the price for the tickets from each of the companies. Well, it’s actually the proportion of the price because we know that each of them have the same full price. So we’ve got company A is five 𝑃, company B is 4.8𝑃, and company C is five 𝑃, where 𝑃 is the full selling price.
So therefore, we can say that as 4.8𝑃 is less than five 𝑃 that company B is the cheapest company and that’s where Sally should buy the tickets from to ensure she gets the cheapest price.