Video: AQA GCSE Mathematics Higher Tier Pack 4 • Paper 2 • Question 15

Each January, there’s a grand monster truck auction, which is the only opportunity to buy or sell monster trucks each year. One January, Grant bought a monster truck for £75000. He competes in the February monster Derby, which happens every year. At the end of each year of ownership, the monster truck loses 6% of its value. Given that Grant wants to sell his monster truck for at least £55000, work out the maximum number of monster derbies that he can enter with this monster truck before he must sell it.

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Video Transcript

Each January, there’s a grand monster truck auction, which is the only opportunity to buy or sell monster trucks each year. One January, Grant bought a monster truck for 75000 pounds. He competes in the February monster Derby, which happens every year. At the end of each year of ownership, the monster truck loses six percent of its value. Given that Grant wants to sell his monster truck for at least 55000 pounds, work out the maximum number of monster derbies that he can enter with this monster truck before he must sell it.

We’re told that Grant buys his monster truck for 75000 pounds in January. He then competes in the February monster derby. And at the end of each year, the truck loses six percent of its value. He needs to sell his monster truck for at least 55000 pounds. So that’s 55000 pounds or more.

Let’s work out then the cost of the monster truck at the end of the first few years of ownership. There are two ways we could do this. We could work out six percent of the value of the truck and then subtract it from the original value. To do this, we begin by finding one percent of 75000. And to find one percent of a number, we divide it by 100. So one percent of 75000 is 75000 divided by 100 which is 750 pounds. Six percent is six times the size of this. It’s 750 multiplied by six which is 4500. Since the monster truck loses six percent of its value each year, we can subtract 4500 from the original. 75000 minus 4500 is 70500 pounds.

Let’s put this information in a table so we can easily keep track. At the end of the first year of ownership, the truck is worth 70500 pounds. And this would mean that Grant could take part in a monster derby in February before selling it in the auction in the following January for 70500 pounds. And what we could do next is repeat this process for year two: finding six percent of the new value of 70500 and then subtracting it from 70500.

Alternatively though, we could use a single decimal multiplier throughout this question. Remember the starting value or the original value is always 100 percent of that number. So to find a six percent reduction, we subtract six percent from 100. And we see that a six percent reduction is the same as finding 94 percent of that number. Now percent means 100. So if we divide 94 by 100, we can see that 94 percent is the same as 0.94. And we can reduce 70500 by six percent by multiplying it by 0.94. 70500 multiplied by 0.94 is 66270 pounds.

We’re going to repeat this process for each year of ownership until we find a value that’s less than 55000 pounds. At the end of the third year of ownership and after three monster derbies, it’s worth 62293 pounds and 80 pence.

For year four, we multiply by 0.94 again and we get 58556.172. Now, this number doesn’t make sense in monetary terms. It’s not the end of the world. We don’t need to know the exact value just when it reaches the price of 55000 pounds. But what we can do is round this number to two decimal places. And we see at the end of the fourth year of ownership, we have 58556 pounds and 17 pence as the cost of that monster truck.

Now for the fifth year of ownership, you might get a slightly different answer. It very much depends whether you round the previous answer. If we didn’t round the previous answer, we would see that the value of the monster truck is 55042 pounds point 80168, which correct to two decimal places is 55042.80. And we can see that it’s very likely that the next reduction in price will take us below 55000.

But let’s double check. We do indeed get a value that’s lower than 55000 pounds. We get 51740 pounds and 23 pence if we round to two decimal places. This means that if Grant does compete in six February monster derbies, his truck will dip below the value of 55000 pounds.

This means then that Grant can compete in five monster derbies before selling his truck for 55042 pounds and 80 pence.

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