# Video: AQA GCSE Mathematics Higher Tier Pack 1 • Paper 2 • Question 10

AQA GCSE Mathematics Higher Tier Pack 1 • Paper 2 • Question 10

02:25

### Video Transcript

Charlotte and Isabel both build a tower using 10 pence coins. Charlotte’s tower has a height of 𝑙 millimeters and Isabel’s tower has a height of 92.5 millimeters. The ratio of the heights of the two towers is two to five. And each 10 pence coin is 1.85 millimeters thick. Calculate the number of 10 pence pieces in Charlotte’s tower.

The first thing we should note is that the ratio of the heights of the two towers is two to five. This is the height of Charlotte’s tower compared to the height of Isabel’s tower. And it’s two to five.

We’re given the height of Isabel’s tower, which is 92.5 millimeters. And we have an unknown value for the height of Charlotte’s tower, represented by the variable 𝑙. We can ask the question “how would we get from five to two? what could we multiply this five by to equal two?”

If we multiply five by two-fifths, we get two. And we know because of this ratio that the heights are in proportion to two to five, we can multiply the height of Isabelle’s tower by two-fifths to find the height of Charlotte’s tower.

The height of Charlotte’s tower equals 92.5 times two-fifths which is 37 millimeters. When we look closely at the question though, we’re trying to calculate the number of 10 pence pieces, not the height of Charlotte’s tower.

We know that each 10 pence coin is 1.85 millimeters thick. The number of 10 pence coins in Charlotte’s tower will be equal to the height of her Tower in millimeters divided by the thickness of the coin in millimeters.

We’ve already calculated the height, 37 millimeters. Each coin is 1.85 millimeters thick. When we divide 37 by 1.85, we get 20.

There were 20 coins in Charlotte’s tower.