Chris is thinking of getting a new mobile phone to use over the next two years. He will either buy the phone with a pay-as-you-go SIM or he will buy the phone on a
contract. The details of both are shown below.
Pay-as-you-go: a one-off charge of 430 pounds plus 1.8 pence per one megabyte used,
where 1000 megabytes is equal to one gigabyte. Contract: a one-off charge of 50 pounds plus 24 pounds per month, which includes up
to one gigabyte of data per month.
On average, Chris uses 0.75 gigabytes of data per month. However, he never uses more than one gigabyte of data in a single month. Over the course of two years, will it be cheaper for Chris to buy the pay-as-you-go
phone or the contract phone? You must show your working.
Let’s start by looking at how much Chris would spend on the phone if he bought it
with the contract. He’d have to pay 50 pounds upfront and then 24 pounds per month for two years since
he never uses more than one gigabyte of data in a single month. Since there are 12 months in one year, this means in two years there will be 12 times
two, which is also equal to 24 months.
Since Chris will be spending 24 pounds per month for two years, this means that we
need to add 24 times 24 to the cost of the contract. And so the cost of the contract is equal to 50 plus 576. And this gives us a total for the cost of the contract over two years of 626
Now, let’s look at how much Chris would spend on the pay-as-you-go phone over two
years. Let’s start by working out how much data Chris will use over the two years. We’re told that on average Chris uses 0.7 gigabytes of data per month. So over the course of two years, which is 24 months, Chris will use 0.75 times 24
gigabytes. And that’s also equal to 18 gigabytes.
Now, to work out how much Chris spends on data, we need to convert this amount into
megabytes since we know the cost of data per megabyte. We’re told in the question that one gigabyte is equal to 1000 megabytes. This tells us that 18 gigabytes is equal to 18 times 1000 megabytes. And this is also equal to 18000 megabytes. This tells us that over the two years Chris will be using 18000 megabytes.
Next, we can work out how much it will cost Chris to use this much data on the
pay-as-you-go SIM. We’re told in the question that it’s 1.8 pence per megabyte used. And so we can find the cost of the data by simply multiplying 18000 by 1.8. And this is equal to 32400 pence. Since there are 100 pennies in a pound, 32400 pence is also equal to 324 pounds.
Now, we can calculate the total cost of the pay-as-you-go phone over two years. Chris will have to pay an upfront cost 430 pounds plus the total amount spent on data
over the two years. So that’s the 324 pounds we calculated earlier. This gives us a total cost of 754 pounds.
As we can see, the pay-as-you-go phone will cost Chris more than the contract phone
since 754 is greater than 626. And so we can conclude that it will be cheaper for Chris to buy the contract