Rick, Selma and Tony are playing a game with counters - Edexcel - GCSE Maths - Question 4 - 2022 - Paper 3

According to the problem, the total number of counters they have together is 54. We can write this as an equation:

$R + S + T = 54$

Substituting $S$ and $T$ with our expressions in terms of $R$, we get:

$R + 2R + (2R - 6) = 54$

Combining like terms, we have:

$R + 2R + 2R - 6 = 54$ $5R - 6 = 54$

Adding 6 to both sides gives: $5R = 60$

Dividing both sides by 5 results in: $R = 12$

Now that we have $R$, we can find the other values:

• Selma's counters: $S = 2R = 2 imes 12 = 24$
• Tony's counters: $T = 2R - 6 = 24 - 6 = 18$

From the problem, we need to find the ratio of the number of counters Rick has to the number of counters Tony has:

$\text{Ratio} = \frac{R}{T} = \frac{12}{18}$

To express it in the form of $1 : p$, we simplify the fraction:

$\frac{12}{18} = \frac{2}{3}$

Thus, we can see that the ratio can be written as:

$1 : \frac{18}{12} = 1 : 1.5$

Consequently, we determine that $p = 1.5$.