algebra puzzle?

[lem0n84]

Q: when a group of girls are put into teams of x, there are two girls left without a team. The same happens with teams of 7 or 8. How many girls are there in the group?

I thought the equation would be:
6x + 2 = 7y + 2 = 8z + 2

Not sure if I'm on the right track. I can't solve it cause there are multiple letters.

Even if i reduce the equation to 6x+2 = 7y+2, I still don't know how to go on solving it.

The answer at the back said 170. But how can you prove this mathematically>?

 

[Deleted member 4993]

Q: when a group of girls are put into teams of x, there are two girls left without a team. The same happens with teams of 7 or 8. How many girls are there in the group?

I thought the equation would be:
6x + 2 = 7y + 2 = 8z + 2

Not sure if I'm on the right track. I can't solve it cause there are multiple letters.

Even if i reduce the equation to 6x+2 = 7y+2, I still don't know how to go on solving it.

The answer at the back said 170. But how can you prove this mathematically>?

Did you mean "six" - instead of "x"?

Did they ask for "minimum" number of girls?

Please post the EXACT & COMPLETE problem.

 

[Dr.Peterson]

Q: when a group of girls are put into teams of 6 [?], there are two girls left without a team. The same happens with teams of 7 or 8. How many girls are there in the group?

I thought the equation would be:
6x + 2 = 7y + 2 = 8z + 2

Not sure if I'm on the right track. I can't solve it cause there are multiple letters.

Even if i reduce the equation to 6x+2 = 7y+2, I still don't know how to go on solving it.

The answer at the back said 170. But how can you prove this mathematically>?

If we let N = 6x + 2 = 7y + 2 = 8z + 2, where x, y, and z are integers, then observe that N - 2 is a multiple of 6, 7, and 8. What is the smallest such N? What other values of N are possible?