# Word problem

### Word problem

The bill for an Indian meal shared by Alan, Helen, Tabitha and Dave was €60. Alan paid a third of the sum of the amounts paid by the others, Helen paid a quarter of the sum of the amounts the others paid, Tabitha paid a fifth of the sum of the amounts paid by the others, how much did Dave pay? Thanks in advance.
Guest

### Re: Word problem

Alan-a , Helen-x , Tabitha-t , Dave-d

a=$$\frac{60-a}{3}$$ ; 3a=60-a ; a=15

x=$$\frac{60-x}{4}$$ ; 4x=60-x ; x=12

t=$$\frac{60-t}{5}$$ ; 5t=60-t ; t=10

d=60-(15+12+10)=60-37=23

Dave-23 euro
Guest

### Re: Word problem

Do you understand what Dave did? The total bill was 60 euro. "Alan paid a third of the sum of the amounts paid by the others". If we let "a" be the amount, in euros, Alan paid, then 60- a, the amount remaining for every one else, is "the sum of the amounts paid by the others". Alan paid 1/3 of that, a= (60- a)/3. That is a single equation to solve for a. Similarly "Helen paid a quarter of the sum of the amounts the others paid" so, letting "h" be the amount Helen paid, h= (60- h)/4. And "Tabitha paid a fifth of the sum of the amounts paid by the others" so, letting t be the amount Tabitha paid- t= (60- t)/5.

Once you figured out how much each of Alan, Helen, and Tabitha paid, add them together to determine how much the three together paid. Subtract that from 60 to find the amount that remains for Dave.
Guest

### Re: Word problem

Yes, i follow the working out of Dave’s . Thanks to both of you for your help, it was much appreciated
Guest