Week 316 (29th September 2023)

Fearne and Leo have both recently started new jobs.  

The ratio of Fearne’s hourly pay to Leo’s hourly pay is 6 : 5. 

After the first month both Fearne and Leo get an increase of £1.50 in their hourly pay.  

The ratio of Fearne’s hourly pay to Leo’s hourly pay after this increase is 13 : 11. 

Work out the hourly pay before the increase for both Fearne and Leo.   

Answer: 

The ratio of initial hourly rates is 6:5 which means their actual rate is in the ratio of 6x : 5x, where x is an unknown multiplier. 

When they receive their increase of £1.50, the ratio is then 6x + 1.5 : 5x + 1.5  

 Since that new ration is equal to 13/11, we can also say that:  

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13(6x+1.5) = 11(5x+1.5)            66x+16.5 = 65x+19.5 

If we take 65x and 16.5 from both sides, we get that x = 3.  

If we substitute x = 3 back into the original ratio of 6x:5x to find their original hourly rate so.. 

6(3) : 5(3) = £18 : £15  

Therefore, Fearne had £18 an hour and Leo had £15 an hour.