Question 1189804
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Part A


Nia made the mistake in line 3
She went from 3+3*4 to 6*4 which is not correct
It's a common mistake students make at first is that they add before multiplying. Refer to PEMDAS or BODMAS or "order of operations" for more information.


Nia should have simplified the 3*4 into 12 first before adding later.
So,
3+3*4 = 3+12 = 15
There are 15 people going on the bus.


One way to draw a picture is to have 3 circles and four dots per circle. That will represent the 3*4 = 12 dancers. Then have 1 dot to represent the driver, and 2 more dots for the coaches. Count out all the dots and you should find there are 15 dots total.
The driver and coaches are not in any of the circles.


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Part B


The 3*4 means we have 3 circles of 4 dots per circle.
If we had say 5 circles, each four dots, then we'd have 5*4 = 20 dots in all the circles combined.


The question is: what if we don't know how many teams there are? Since this is unknown, we refer to it as the variable n.


The general rule is that having n circles means there are 4n dots overall in the circles alone. Simply multiply the number of dots per circle with the number of circles.


The original expression of
1+2+3*4
would turn into
1+2+n*4
which is the same as
1+2+4n
since we can multiply in any order


Then to tidy things up just a bit, the 1+2 becomes 3
So we end up with 3+4n as the expression to reprsent the total number of people going on the bus. Where n is the number of teams.


The expression 3+4n means we have 4 dots per circle (n number of circles) and 3 extra dots outside all the circles to represent the 1 driver + 2 coaches.



Answer: 3+4n

 
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Part C


If we had 2 coaches per team, and not just 2 coaches flat, then we'd have 2n coaches for n number of teams.


The expression 
1+2+4n
would become
1+2n+4n
and that simplifies to
1+6n


Each circle now has 6 dots to represent the 4 dancers + 2 coaches per circle. Like before, n is the number of teams and it's some positive whole number (eg: n = 5). Outside all the circles is one single dot to represent the driver.


Answer: 1+6n
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