Tadams052012
New member
- Joined
- Oct 29, 2018
- Messages
- 8
Hi there,
This is my second post on this forum, I'm self studying Algebra from a book called: Teach Yourself Algebra: A Complete Introduction. Since the last problem you guys helped me with I've been cruising along and have reached 'linear equations' something I've been quite enjoying, until this question that is...
11. A teacher distributes $2 among 20 children, giving 5 cents to some and 25 cents each to the rest. How many children received 25 cents each?
Now my difficulty here is not solving the problem per se, I've done so using mental reasoning (a kind of trial and error method where I go through different combinations of fives and twenty-fives until they make up twenty with their total equaling two-hundred cents of course), the answer is five.
No, my problem is putting this conundrum into the form of a linear equation and solving it algebraically on paper. This is what I need to be able to do, since obviously, once the problems become more complex my patchy mental trial and error is no longer going to be reliable or even workable.
Is there anyone out there who might be able to take me through the process of solving this problem using a linear equation?
Just to illustrate my thought process and perhaps give you an inkling of where I'm going wrong: the first thing I'm doing is looking for the unknown to be ascertained, which is obviously the number of children receiving 25 cents, I assign this a letter - X.
Now where my problem begins is that there is also another unknown in this situation: the number of children who received 5 cents, and the two unknowns are interdependent, so it seems I must give this one a letter also - Y.
Now having two unknowns in my equation seems to throw up all kinds of problems since to find the value of one it needs to be isolated on one side with a numerical value on the other. This means removing the other of the two unknowns from the equation, which seems impossible at least as long as it remains in letter form i.e. subtract Y from one side means to subtract it from the other which means you then have -Y on the other side.
Here are the only things resembling linear equations I've been able to formulate:
X+Y=20
and
25X + 5Y = 200
Any help would be much appreciated.
Many thanks,
Tom.
This is my second post on this forum, I'm self studying Algebra from a book called: Teach Yourself Algebra: A Complete Introduction. Since the last problem you guys helped me with I've been cruising along and have reached 'linear equations' something I've been quite enjoying, until this question that is...
11. A teacher distributes $2 among 20 children, giving 5 cents to some and 25 cents each to the rest. How many children received 25 cents each?
Now my difficulty here is not solving the problem per se, I've done so using mental reasoning (a kind of trial and error method where I go through different combinations of fives and twenty-fives until they make up twenty with their total equaling two-hundred cents of course), the answer is five.
No, my problem is putting this conundrum into the form of a linear equation and solving it algebraically on paper. This is what I need to be able to do, since obviously, once the problems become more complex my patchy mental trial and error is no longer going to be reliable or even workable.
Is there anyone out there who might be able to take me through the process of solving this problem using a linear equation?
Just to illustrate my thought process and perhaps give you an inkling of where I'm going wrong: the first thing I'm doing is looking for the unknown to be ascertained, which is obviously the number of children receiving 25 cents, I assign this a letter - X.
Now where my problem begins is that there is also another unknown in this situation: the number of children who received 5 cents, and the two unknowns are interdependent, so it seems I must give this one a letter also - Y.
Now having two unknowns in my equation seems to throw up all kinds of problems since to find the value of one it needs to be isolated on one side with a numerical value on the other. This means removing the other of the two unknowns from the equation, which seems impossible at least as long as it remains in letter form i.e. subtract Y from one side means to subtract it from the other which means you then have -Y on the other side.
Here are the only things resembling linear equations I've been able to formulate:
X+Y=20
and
25X + 5Y = 200
Any help would be much appreciated.
Many thanks,
Tom.