a student spends no more than 2 hours on his math and English homework If math takes about twice as long as English what is the maximum time that the student can spend on English

Question

solomonzelman · Answer

(in our calculations)
~   label the Math Homework with letter  M
~   label the English Homework with letter E.

solomonzelman · Answer

you know that all of the homework together is done in no more than 2 hours.

No more than 2 hours, means that the time he needs to do all of his homework is less than or equal to 2 hours. (which gives as)
$\large\color{black}{  M+E\le2         }$  
Now, we know that Math homework takes twice as long as English. (gives us)
$\large\color{black}{   2E=M                  }$

anonymous · Answer

Is that it

solomonzelman · Answer

Solve the system, but I would prefer that you show your work here....

anonymous · Answer

I still don't get it can 
You show me

solomonzelman · Answer

do you get how I extracted/obtained the 2 equations above?

$\large\color{black}{  M+E\le2         }$  
$\large\color{black}{   2E=M                  }$

solomonzelman · Answer

I mean below.

solomonzelman · Answer

I am just asking, do you know where,  $\large\color{black}{  M+E\le2         }$   and   $\large\color{black}{   2E=M                  }$    are coming from (in this problem) ?

anonymous · Answer

Yes but i m asking where's the answer

anonymous · Answer

What's

solomonzelman · Answer

okay, substitute  $\large\color{black}{  2E }$  for $\large\color{black}{  M   }$  into  $\large\color{blue}{  M+E\le2         }$  and solve for E.

anonymous · Answer

OK now what

solomonzelman · Answer

have you done that? can you show me what equation do you get after that substitution?

anonymous · Answer

2e+e≤2

solomonzelman · Answer

yes.

solomonzelman · Answer

you have:  $\large\color{black}{  2e+e\le2         }$   .   Now, add like terms on the right hand side

solomonzelman · Answer

I mena on the left side, ... sorry.

anonymous · Answer

Ok

solomonzelman · Answer

what do you get?

anonymous · Answer

1

solomonzelman · Answer

wait, you have
$\large\color{black}{  2e+e\le2         }$
add the $\large\color{blue}{  e         }$s and you get?

anonymous · Answer

is the overall Answer 1

solomonzelman · Answer

for e?

solomonzelman · Answer

you are solving for the maximum number of time that the student can do his English for,

solomonzelman · Answer

the answer is not 1 hour.

solomonzelman · Answer

when you add like terms, you get,
$\large\color{black}{  3e\le2         }$       correct?

solomonzelman · Answer

if so, then divide both sides by 3, and tell me what you got.

anonymous · Answer

4 i just kidding