# Video: GCSE Mathematics Foundation Tier Pack 1 • Paper 3 • Question 22

GCSE Mathematics Foundation Tier Pack 1 • Paper 3 • Question 22

02:55

### Video Transcript

Mr. Gudge had 10 litres of fuel in his car at the beginning of January when he completely refilled the tank. The cost to refill the car was 60 pounds, and the cost of fuel was one pound 20 per litre. At the beginning of June, he had eight litres of fuel in his car when he completely refilled the tank. The price of fuel had risen by 10 percent. How much did the June refill cost?

We can begin by working out the total number of litres that Mr. Gudge’s fuel tank holds. The question says that the car cost a total of 60 pounds to fill and that the price of fuel was one pound 20 per litre.

To calculate the number of litres he bought then, we’ll need to divide 60 by one pound 20. 60 divided by one pound 20 is 50, so he bought 50 litres of fuel. Remember though that there were already 10 litres in his tank. So this means his fuel tank must take a total of 60 litres. 50 plus 10 is 60.

At the beginning of June, we’re told that he had eight litres of fuel in his car. That means, to calculate how many litres he put into the tank to fill it, we’ll subtract eight from 60, since 60 was the total amount of litres his fuel tank could hold. 60 minus eight is 52 litres. He needed to buy 52 litres in June to fill his tank.

Next, we’re told that the price increases by 10 percent. There are a number of ways we can work out a 10-percent increase. The first method is to work out 10 percent of one pound 20. We find 10 percent by dividing the original number by 10. One pound 20 divided by 10 is 0.12. Since it’s an increase, we’ll add this onto the original price. One pound 20 plus 0.12 pounds, or 12P, is equal to one pound 32 per litre.

Alternatively, if we think of the original as 100 percent, then we can see that a 10-percent increase can be calculated by adding 10 and 100 to get 110 percent. Since “percent” means “out of 100,” we can write 110 percent as 110 over 100. We then multiply the original number by this fraction, which once again gives us a value of one pound 32 per litre.

Now that we know the cost of one litre, we can work out how much he paid in June. He bought 52 litres. 52 multiplied by one pound 32 is 68 pounds 64. The June refill cost Mr. Gudge 68 pounds 64.