Simultaneous eqn question that is embarrassingly stumping me! 230 students, 29 staff

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Simonsky

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What I love about maths is when I think I'm making progress and what should be a simple question reveals yet another cognitive deficit crushing my ego and embedding my face in more 'humble pie.' here's the latest manifestation:

230 school students and 29 staff are going on a school trip. They travel by large and small coaches. The large coaches seat five and the small ones seat 39. If there are no spare seats and five coaches are to make the journey, how many of each coach are used.

Well, as this question is in a section on simultaneous equations I thought I needed to extract two equations from this so I came up with :

55L +39S = 259 (L=large;S=small seats) and the Other equation being L+S = 5 (the total number of coaches)

So I then multiplied the latter equation by 39 to get a number that eliminates one of the variables to get:

55L +39S = 259

minus 39L+39S = 195

= 55L = 64. But that can't be right. Seem to have a brain 'freeze' on this for some reason. I've probably formulated the wrong equations-I've generally not found simultaneous equation questions too difficult can't see why this one has got me hitting a 'cognitive wall.'
 
Simonsky said:
What I love about maths is when I think I'm making progress and what should be a simple question reveals yet another cognitive deficit crushing my ego and embedding my face in more 'humble pie.' here's the latest manifestation:

230 school students and 29 staff are going on a school trip. They travel by large and small coaches. The large coaches seat five and the small ones seat 39. If there are no spare seats and five coaches are to make the journey, how many of each coach are used.

Well, as this question is in a section on simultaneous equations I thought I needed to extract two equations from this so I came up with :

55L +39S = 259 (L=large;S=small seats) and the Other equation being L+S = 5 (the total number of coaches)

So I then multiplied the latter equation by 39 to get a number that eliminates one of the variables to get:

55L +39S = 259

minus 39L+39S = 195

(55 - 39)L = (259 - 195).

(16)L = (64).



But that can't be right. Seem to have a brain 'freeze' on this for some reason. I've probably formulated the wrong equations-I've generally not found simultaneous equation questions too difficult can't see why this one has got me hitting a 'cognitive wall.'
Click to expand...
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There is nothing wrong with your intelligence or aptitude. You skipped steps. Skipping steps is the cause of so many errors.

You did perfectly the hard step of translating the problem into math and then messed up by skipping steps in the simple mechanical part.

\(\displaystyle L + S = 5.\)

\(\displaystyle 55L + 39S = 230 + 29 = 259.\)

\(\displaystyle \therefore 39L + 39S = 39 * 5 = 195.\)

\(\displaystyle therefore (55L + 39S) - (39L + 39S) = 259 - 195 \implies\)

\(\displaystyle 55L - 39L = 64 \implies 16L = 64 \implies L = \dfrac{64}{16} = 4 \implies\)

\(\displaystyle 4 + S = 5 \implies S = 5 - 4 = 1.\)

Check

\(\displaystyle 4 * 55 + 39 = 220 + 39 = 259.\)

Does it take more time? Yes. Does it avoid silly mistakes? Yes.

If you are going to skip steps, it is really important to check your work. Then, if you did make a mistake, you can go back and do it over without skipping steps. It is important to do it over without skipping any steps rather than just skipping the same steps repeatedly. If you made a mistake when skipping a step, you are extremely unlikely to catch it when you skip it again.

So in fact I tend to skip steps all the time to save time but always check my work. If it does not check, then I go back and do it step by step until I find the error or errors.
 
So in fact I tend to skip steps all the time to save time but always check my work. If it does not check, then I go back and do it step by step until I find the error or errors.[/QUOTE]

Thanks JeffM and Subotash-much appreciated. Wow, what a silly oversight not subtracting the L bit! I think I was content to have translated it into the two equations that I rested on my laurels and descended into sloppiness. Something I do all too often! Another lesson in trying to maintain attentiveness.
 
Simonsky said:
So in fact I tend to skip steps all the time to save time but always check my work. If it does not check, then I go back and do it step by step until I find the error or errors.
Click to expand...

Thanks JeffM and Subotash-much appreciated. Wow, what a silly oversight not subtracting the L bit! I think I was content to have translated it into the two equations that I rested on my laurels and descended into sloppiness. Something I do all too often! Another lesson in trying to maintain attentiveness.[/QUOTE]


Apologies for misspelling 'Subhotosh' I was doing it from memory-another case of not cheking first!
 
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