7 Consecutive numbers: 1/4 of smallest is 5 less than 1/3 of largest

[Joanster1963]

Hi, my niece has some homework which ive been helping her with and i can work out the answer easy enough but by using trial and error really. I was wondering whether there was a way or formula which can be used to solve the problem properly? So she knows for future questions.
Q: in a sequence of 7 consecutive numbers a quarter of the smallest number is five less than a third of the largest number. What is the value of the smallest number?

 

[Deleted member 4993]

Hi, my niece has some homework which ive been helping her with and i can work out the answer easy enough but by using trial and error really. I was wondering whether there was a way or formula which can be used to solve the problem properly? So she knows for future questions.
Q: in a sequence of 7 consecutive numbers a quarter of the smallest number is five less than a third of the largest number. What is the value of the smallest number?

Let the consecutive numbers be: S, S+1, S+2, S+3, S+4, S+5, S+6
Then,
S/4 = (S+6)/3 - 5

Solve for 'S'.

 

[stapel]

Hi, my niece has some homework which ive been helping her with and i can work out the answer easy enough but by using trial and error really. I was wondering whether there was a way or formula which can be used to solve the problem properly? So she knows for future questions.
Q: in a sequence of 7 consecutive numbers a quarter of the smallest number is five less than a third of the largest number. What is the value of the smallest number?

You've posted this to "Arithmetic", which suggests that the student is somewhere in K-6 studies, not having seen any algebra yet. This limits possible solution methods severely. Are you sure that she hasn't done any algebra at all? Thank you!