Hardest level SAT math problem

[shotgunbob]

Homework Statement

A small company has some free movie tickets to distribute to its employees. If each employee gets 5 tickets, there will be 15 left over. If 5 employees will receive 7 tickets, and none will be left over. How many tickets does the company have?

Homework Equations

Algebra/logic and reasoning

The Attempt at a Solution

I got 5x+15=5x-25

 

[Pellefant]

Your formulation of the problem confuse me ...

2 unknowns 2 equations

x=number of employees
b= total number of tickets

x*5=b-15

But the next line i do not understand ...
If 5 employees will receive 7 tickets, and none will be left over.

 

[shotgunbob]

whoops! Sorry! it should be:

If 5 employees decide not to take any tickets, all the other employees will receive 7 tickets, and none will be left over.

 

[Pellefant]

whoops! Sorry! it should be:

If 5 employees decide not to take any tickets, all the other employees will receive 7 tickets, and none will be left over.

Based on that i get the second equation as ...

(x-5)*7=b

 

[HallsofIvy]

This is actually VERY easy.
Pellefant almost got there, he just didn't answer the question.x

Yes, and he didn't because this is a homework and coursework question and he knew he shouldn't!

 

[Redbelly98]

stopchair, it sounds like you're not familiar with the rules at our forum:

"On helping with questions: Any and all assistance given to homework assignments or textbook style exercises should be given only after the questioner has shown some effort in solving the problem. If no attempt is made then the questioner should be asked to provide one before any assistance is given. Under no circumstances should complete solutions be provided to a questioner, whether or not an attempt has been made."

(from https://www.physicsforums.com/showthread.php?t=5374 )

 

[Gregg]

Homework Statement

A small company has some free movie tickets to distribute to its employees. If each employee gets 5 tickets, there will be 15 left over. If 5 employees will receive 7 tickets, and none will be left over. How many tickets does the company have?

Homework Equations

Algebra/logic and reasoning

The Attempt at a Solution

I got 5x+15=5x-25

let employees = e
let number of tickets = t

you might have something like

1. t - 5e = 15
2. t - 7(e-5) = 0

The question asks how many tickets they have, you need to somehow eliminate the unknown.

Spoiler

Work it out then

 

[autrizzle]

Well its really not that hard,

I would set the two equations for the total number of tickets(y) based on the total number of employees (x)

y= 5x+15
y=7(x-5)

Based on that, you can find number of employees and then proceed to ur solution (the number of tickets). gl with SAT. xD.