Question

Josh and his friends bought vanilla wafers for $4 per packet and chocolate wafers for $1 per packet at a carnival. They spent a total of $45 to buy a total of 27 packets of wafers of the two varieties.

Part A: Write a system of equations that can be solved to find the number of packets of vanilla wafers and the number of packets of chocolate wafers that Josh and his friends bought at the carnival. Define the variables used in the equations. (5 points)

Part B: How many packets of chocolate wafers and vanilla wafers did they buy? Explain how you got the answer and why you selected a partic

Answer 1

@Michele_Laino can you help me on this problem also?

Answer 2

ok!

Answer 3

yea thank you!

Answer 4

the system which models your problem is:
\[\Large \left\{ \begin{gathered}
x + y = 27 \hfill \\
4x + y = 45 \hfill \\
\end{gathered} \right.\]
where x is the number of packets of vanilla wafers, whereas y is the number of packets of chocolate wafers

Answer 5

a)

$4v + $1c = $45
v + c = 27
v = vanilla wafers
c = chocolate wafers

Answer 6

@Michele_Laino what does the x and y stand for. like v is vanilla and c is choclate?

Answer 7

yes!
x=v
and y=c

Answer 8

ok wanted to be sure:)

Answer 9

ok!

Answer 10

so know what step is next?

Answer 11

now*

Answer 12

we have to solve the first equation for y, for example, so we get:
\[y = 27 - x\]

Answer 13

then we can substitute into the second equation:
\[4x + \left( {27 - x} \right) = 45\]

Answer 14

please solve that equation for x

Answer 15

x=6

Answer 16

or 6 vanilla

Answer 17

that's right!

Answer 18

b)
solve by elimination:

1)
4v + c = 45
-1(v + c) = -1(27)

2) Distribute
4v + c = 45
-v - c = -27

3) Combine like terms:
3v =18

4) Solve for v:
v = 6

5) plug v = 6 back into your original equation:
6 + c = 27

6) solve for c:
c = 21


v=6
c=21

Answer 19

now we can substitute x=6, into this expression:
\[\Large y = 27 - x = 27 - 6 = ...?\]

Answer 20

what do you get?

Answer 21

21

Answer 22

ok! So, the solution of your system is:
x=6, and y=21

Answer 23

sweet. can you medal @thekefentse for me so he can get an award? ill medal you

Answer 24

ok!

Answer 25

than you:) also im probabley going to have mabe like two more questions if you can help me with them. ill post new and tag you

Answer 26

ok!

Answer 27

Awesome! I hope i helped you to learn as well as @Michele_Laino

Answer 28

@thekefentse ima post new question do you think you and @Michele_Laino can help on them if yall dont mind?

Answer 29

I don't mind

Answer 30

thank you. tag ya in a bit

Answer 31

alright