Question

at a barbeque there were 250 dinners served. children's plate were $1.50 each and adults plates were 2.00 each. if the total money collected was $441, how many of each type of plate was served?

Answer 1

Hey :)

Let \(\large\rm C\) represent `the number of child plates`.
Then the `money collected from all of the children's plates` would be \(\large\rm 1.50C\).
The number of plates C times 1.50 per plate.

Also, let \(\large\rm A\) represent `the number of adult plates`.
Then the `money collected from all of the adult plates` would be \(\large\rm 2.00A\).
The number of plates A times 2.00 per plate.

Answer 2

The total `number of plates` sold was 250.
Adult plates plus child plates equals our total.
\[\large\rm A+C=250\]

Answer 3

The total `money collected` was 441.
Adult money collected plus children money collected equals our total.\[\large\rm 2A+1.5C=441\]

Answer 4

This gives us a system of `two equations`
with `two unknowns`

Answer 5

You can solve the system using a variety of methods.
You're probably familiar with either `substitution` or `elimination`.

Answer 6

Confused? :o

Answer 7

A little, so there are two equations we need to figure out?

Answer 8

There are two variables you need to figure out, A and C.
You have to combine the equations in same way.

Answer 9

that's where i need help

Answer 10

\[\large\rm A+C=250\]\[\large\rm 2A+1.5C=441\]
Substitution or Elimnation? :d
No preference?

Answer 11

oh wait i think i know now!

Answer 12

Let's do elimination

Answer 13

To do elimination, we need one of the variables to `match up` in both equations.
It's much easier to match to the larger number, rather than trying to go backwards.

So, notice that the second equation has a 2A.
Our first equation has only A.

We need to multiply the first equation by something to match up the A's.

Answer 14

yess i did that she leads us to 2A+2C=4.00

Answer 15

then i change the signs of the bottom ones

Answer 16

Woops! :O
That looks a little off.\[\large\rm 2(A+C=250)\]\[\large\rm 2A+2C=500\]Something like that, ya?

Answer 17

yeah that's what i meant is that i was looking at the 2.00 of adults sorry

Answer 18

\[\large\rm \quad~2A+2C~~~=500\]\[\large\rm -(2A+1.5C=441)\]-----------------------

And you wanted to negate the second equation like this?
And then combine, ya?

Make sure you change the sign of EVERYTHING in the second equation,
not just the A's :)

Answer 19

Yess and then i got C= 118?

Answer 20

Good! :)

Any ideas on how to find A?

Answer 21

yesss and i got A= 132

Answer 22

Yayyy good job! ୧ʕ•̀ᴥ•́ʔ୨

Answer 23

132 adult plates were served,
118 children plates were served

Answer 24

Thank you :)