A group has an equal number of adults and children. When n oranges are given to the group, each adult gets two oranges while each child gets one orange and there are still 5 oranges left. Write an algebraic expression for the number of oranges given to the adults.

The list price of a camera was w dollars. Paul bought the camera for $35 less than the list price. If the sales tax was 8 %, how much did paul pay for the camera including the sales tax?

There were m visitors in an exhibition on the first day and 1200 fewer visitors on the second day. On the third day, the number of visitors was 30% greater than the number of visitors on the second day. What was the average number of visitors over the three days?

Thanks

Mathcalc

mathcalc
Dec 3, 2015

#3**+10 **

There were m visitors in an exhibition on the first day and 1200 fewer visitors on the second day. On the third day, the number of visitors was 30% greater than the number of visitors on the second day. What was the average number of visitors over the three days?

The average number is given by :

[m + (m - 1200) + (m - 1200)(1.30 ] / 3 =

[ 2m + 1.30m - 1200 - 1560] / 3 =

[3.3m - 2760] / 3 =

[1.1 m - 920 ]

Edit for a slight error.........

CPhill
Dec 3, 2015

#1**+10 **

A group has an equal number of adults and children. When n oranges are given to the group, each adult gets two oranges while each child gets one orange and there are still 5 oranges left. Write an algebraic expression for the number of oranges given to the adults.

The number of oranges given to the adults = 2x = n - x - 5 where x = the number of children = the number of adults

CPhill
Dec 3, 2015

#2**+10 **

The list price of a camera was w dollars. Paul bought the camera for $35 less than the list price. If the sales tax was 8 %, how much did paul pay for the camera including the sales tax?

The amount paid = A = (w - 35)(1.08)

CPhill
Dec 3, 2015

#3**+10 **

Best Answer

There were m visitors in an exhibition on the first day and 1200 fewer visitors on the second day. On the third day, the number of visitors was 30% greater than the number of visitors on the second day. What was the average number of visitors over the three days?

The average number is given by :

[m + (m - 1200) + (m - 1200)(1.30 ] / 3 =

[ 2m + 1.30m - 1200 - 1560] / 3 =

[3.3m - 2760] / 3 =

[1.1 m - 920 ]

Edit for a slight error.........

CPhill
Dec 3, 2015

#5**+5 **

Hi Mathcalc,

A group has an equal number of adults and children.

Let K be the number of children (kids) Sinve there is the same number of adults then K is the number of adults too

When **n oranges** are given to the group, each adult gets two oranges while each child gets one orange

and there are still 5 oranges left.

The adults get 2 oranges each that is 2K oranges and the children get 1 orange each, that is K oranges and there is 5 oranges left over.

SO

n = 2K+K+5

Write an algebraic expression for the number of oranges given to the adults.

n=3K+5

n-5=3K

K=(n-5)/3

but the adults get twice this many oranges so the adults get

2(n-5)/3 oranges.

CPhill's answer is the same, he has just not simplified it. and i used a k instead of an x

Does that help ?

Do you want me to discuss the others as well. OR maybe if you need more explanation, CPhill might like to help you.

We like it when people ask us about our answers. It means we are really teaching someone :))

(Sometimes we wonder if anyone even reads an answer)

Melody
Dec 4, 2015

#6**+5 **

I kind of get it now, it's just I didn't know how CPhill figured out his answers. I'll try and ask him.

Thanks so much

Mathcalc

mathcalc
Dec 4, 2015

#7**0 **

Melody,

Can u please also explain the other 2? I sent a message to CPhill as well to explain them. I just want to see which method would work best for me.

Sorry if I keep bothering you.

Thanks

Mathcalc

mathcalc
Dec 4, 2015

#8**+5 **

The list price of a camera was w dollars. Paul bought the camera for $35 less than the list price. If the sales tax was 8 %, how much did paul pay for the camera including the sales tax?

Notice that 8% tax can be written as .08

And if he gets the camera for 35 dollars less than list price he spends (w - 35) dollars.....and this is before the tax is added.....

So......he pays this price plus 8% of the price in tax......in math terms we have

Price + Tax =

(w - 35)(1) + (w - 35)(.08) = [factor out the (x - 35)]

(w - 35) [ 1 + .08] =

(w - 35) (1.08)

Does that make sense???

CPhill
Dec 4, 2015

#9**+5 **There were m visitors in an exhibition on the first day and 1200 fewer visitors on the second day. On the third day, the number of visitors was 30% greater than the number of visitors on the second day. What was the average number of visitors over the three days?

1st day = m

2nd day = m - 1200

3rd day = the number the second day plus 30% more = [m - 1200] + .30[m - 1200] = (1.30)[m- 1200]

So....we add the attendance over 3 days and divide by 3 and we have

[m + ( m- 1200) + (1.30)( m - 1200) ] / 3 we could leave it like this, but let's simplify

[2m - 1200 + 1.30m - 1560] / 3 combine like terms on the top

[3.3m - 2760] / 3 note that we can write this as :

[3.3m ] / 3 - 2760/3 =

1.1m - 920

I see where you got confused......I made a slight error in my first post by keeping the "divided by 3" part in at the last.....I'll edit that out right now.....!!!!!

Does that help???

CPhill
Dec 4, 2015

#10**0 **

Thanks Chris,

**Mathcalc:** Before I answer any more I want you to examine CPhill's answers **and tell him whether you understand.**

If you do not, try to be specific about what you do not understand.

These are tricky questions I think, and getting the concepts involved is difficult.

If you try very hard to understand and you still do not **I shall take a look at them with you.**

I think Chris will be ok with that. We both want you to learn the best you can :)

Melody
Dec 5, 2015