There are 20 coins in a pot - OCR - GCSE Maths - Question 7 - 2017 - Paper 1

Let the number of 5p and 10p coins be represented as $z$ and $w$, respectively.

From our earlier calculations, we have: $x + y + z + w = 20$ $6 + 8 + z + w = 20$ This gives us: $z + w = 6$

Next, we consider the total value: $1x + 2y + 5z + 10w = 57$ Substituting the known values: $1(6) + 2(8) + 5z + 10w = 57$ Solving gives: $6 + 16 + 5z + 10w = 57$ $5z + 10w = 35$ Dividing through by 5: $z + 2w = 7$

Now we have a system of equations:

1. $z + w = 6$
2. $z + 2w = 7$

From equation 1, we can express $z$ as: $z = 6 - w$ Substituting into equation 2: $6 - w + 2w = 7$ This simplifies to: $6 + w = 7$ Thus: $w = 1$ Substituting back, we find: $z = 6 - 1 = 5$

In conclusion, the number of coins is as follows:

• 1p coins: 6
• 2p coins: 8
• 5p coins: 5
• 10p coins: 1