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Mukaro Mukaro
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Posts: 13
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11 years ago
Q: A high school marching band of 205 students went to a competition. They took 9 vehicles, some cars and some buses. Find the number of cars and the number of buses they took if each car holds 5 students and each bus hold 45 students. The answer is 5 cars and 4 busses. 

Please explain process of setting equation, solving and checking. Thank you in advance, I am lost.
Post Merge: 11 years ago

Post title should read: Solve this linear Equation using elimination OR substitution
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bio_manbio_man
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Educator
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Posts: 33341
11 years ago
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Mukaro Author
wrote...
11 years ago
Wow, I am amazed.

I was able to set up the problem but was lost soon after doing c + b = 9, then 5c + 45b = 205. I did not remember the rule to set-up c = 9 - b.

I was able to follow you up to 45 + 40b = 205

I am not clear how you did 40b = 205 - 45 and down to 4.

Also, is this considered the "elimination" method?

Thanks again. 

wrote...
Educator
11 years ago
No, this is definitely substitution.

I went from c + b = 9 to c = 9 - b because I wanted to isolate one of the variables. I could have also done b = 9 - c. Technically what I did in the first example was I moved the + b to the other side. If you move + b to the other side (over the equal sign), the symbol changes from positive to negative. That's what it becomes 9 minus b, instead of 9 plus b.

At this stage, 45 + 40b = 205, I want to isolate for b. Notice how 45 is on the same side as the variable I want to isolate for. To get rid of it, I bring it over. Notice how the 45 is also positive (there is no negative sign in front of it). If I move it over, it becomes -45:

40b = 205 - 45

If you subtract 45 from 205, you get 160:

40b = 160

Now, to isolate for b, you need to get rid of 40, which is sort of "glued" to it. To reverse this, we divide both sides by 40:

40b = 160
-----    ------
40     40

b = 160 divided by 40 is 4.
Mukaro Author
wrote...
11 years ago
Thank you so much, I am actually starting to get a clear picture on how this works. I am not there yet but your explanation has been very, very helpful. Thank you again!
wrote...
Educator
11 years ago
Thank you so much, I am actually starting to get a clear picture on how this works. I am not there yet but your explanation has been very, very helpful. Thank you again!

Any time... post more if you need it.
wrote...
11 years ago
Thank you!  Smiling Face with Open Mouth
MizuSeirei
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