i spent 20 mins on this problem?i need guidance?

Question

can some guide me into this problem, I totally don't understand.
i did the calculations and keep getting D.$4.50. would that be the correct answer?

Kara and Sonny went to see a movie at the local theater.

Kara paid $13.00 for 1 large box of popcorn and 2 large soft drinks.

Sonny paid $8.50 for 1 large box of popcorn and 1 large soft drink.

In the system of equations below, p represents the cost of 1 large box of popcorn and s represents the cost of 1 large soft drink.

p + 2s = 13.00
p + s = 8.50

What is the value of p, the cost of 1 large box of popcorn?

A. $4.00
B. $4.25
C. $4.30
D. $4.50

Answer 1

Like you said (or stated), we have these 2 equations formed
p + 2s = 13.00
p + s = 8.50
,where p = the box of popcorn and s = the soft drinks
If we subtract the 2 equations:
p + 2s = 13.00
-p + s = 8.50,
We get s=4.50 (p-p cancels out)

Subbing this value of s into the 2nd equation again, we get
p + s = 8.50
p + 4.50 = 8.50
p= 4.00

So the value of the popcorn is $4.00 [Answer : A]

Answer 2

p + 2s = 13.00
p + s = 8.50

these equations are correct.when you subtract the 2nd equation from the 1st you get s = 4.50 - but this is the price of the soda, not the popcorn.

Since p + s = 8.50 and s = 4.50 then p = 4.00 so the answer is (a).

Answer 3

We will subtract the second equation from the first to find the price of one large soda
(p + 2s = 13.00)
-(p + s = 8.50)
=
s=4.50
Plug this number into the second equation to find the price of the popcorn
4.50+p=8.50
p=4.00 (subtract 4.50 from each side)
So the answer is A

Answer 4

Using the process of elimination:

1. Multiply the bottom equation by -2 to cancel out the 's'.

p + 2s = 13
-2p - 2s = -17

2. Add the equations together.

-p = -4
p = 4

The answer is A. $4.00

Answer 5

A. $4.00
1) p + 2s = 13.00
2) p + s = 8.50
subtract equation 2 from equation 1
s = 4.50
substitute 4.50 for s in equation 2
p + 4.50 = 8.50
p = 8.50 - 4.50 = 4.00

Answer 6

$ P= cost of popcorn
$ D = cost of drinks

1P + 2D = 13
1P + D = 8.5

D = 4.5
P = 4

Drink costs $4.50
Popcorn costs $4.00

OPTION A

Answer 7

s = 8.50 - p

p + 2(8.50 - p) = 13.00
p + 17 - 2p = 13.00
-p = 13 - 17
p = 4

I got A. $4.00.

Answer 8

you have set up the equations correctly, and that is the first step.

now, you can either use subsitution or solve simultaneously.

by sub, set s=8.5-p and sub into the first equation:

p+2(8.5-p)=13
p+17-2p=13
p=4

or, solve simultaneously:

subtract equations and get:

(p-p)+(2s-s)=13-4.5
s=4.5, so p=4

Answer 9

Answer A

Answer 10

A] $4.00