Week 348 (7th June 2024)

Richard, Sam and Tom are playing a game with counters.   

Richard has some counters.   

Sam has twice as many counters as Richard.  

Tom has 6 counters less than Sam.   

In total they have 54 counters.   

If the ratio of Richard’s counters to Tom’s is 1 : p, find the value of p.  

Answer:  

If n is the number of counters Richard has then Richard has n counters, Sam has 2n counters and Tom has (2n-6) counters.

To find n we can set up an equation for the total number of counters:

n + 2n + 2n – 6 = 54 …. And then solve for n

5n – 6 = 54        5n = 60        n = 12, So Richard has 12 counters. This means Tom has 2(12) – 6 = 18 counters.

The ratio for this would be 12 : 18. We can divide both sides by 12 to get in the form 1 : p. This gives us a ratio of 1 : 1.5 therefore p = 1.5