Equations with three variables

warsilver

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Here's the question, I'm confused because I thought all the answers were wrong. One has to be right so.... help.

Dave is buying pizza and soda. Suppose that a slice of pizza and a can of soda each cost $4. Let E represent the amount in dollars that Dave spends on pizza and soda. If Dave buys P slices of pizza and S cans of soda, which of the following equations correctly describes the amount of money he spends?
a) 4E = P + S
b) E = 4P + S
c) E = P + 4S
d) E = P + S
e) E = 4P + 4S

I also need to rearrange the right answer so that S is written in terms of E and P.
 
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imho, you are correct that none of the given answers are true..

if p=slice pizza and s= can of soda and E=dollar (why not ($)), from your description...

\(\displaystyle p+s=8E\)

which does not agree with any of (a) to (e)

There again, if you meant
a slice of pizza and a can of soda each cost $4

as

(a slice of pizza and a can of soda) cost $4 (i.e. combined cost)

then \(\displaystyle p+s=4E\) so (a) would be correct.

I will leave you to re-arrange...

Pro
 
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If it helps, these are the possible answers to the second part of the question...
  1. S = E – P
  2. S = (1/4)E – P
  3. S = E – 4P
  4. S = P + E
  5. S = 4E – 4P
 
Here's the question, I'm confused because I thought all the answers were wrong. One has to be right so.... help.

Dave is buying pizza and soda. Suppose that a slice of pizza and a can of soda each cost $4. Let E represent the amount in dollars that Dave spends on pizza and soda. If Dave buys P slices of pizza and S cans of soda, which of the following equations correctly describes the amount of money he spends?
a) 4E = P + S
b) E = 4P + S
c) E = P + 4S
d) E = P + S
e) E = 4P + 4S

I also need to rearrange the right answer so that S is written in terms of E and P.

I notice that you've edited this posting...so I wonder if you CHANGED the possible answer choices (since you originally thought none were correct and one of the responders agreed with you.)

If a slice of pizza costs $4 and Dave buys P slices, then the cost of the pizza slices would be "cost of one slice multiplied by the number of slices," or 4P.

If a can of soda costs $4 and Dave buys S cans of soda, then using the same type of reasoning we used for the pizza, the cost of the soda would be 4S.

E is the total that Dave spent....

E = cost of the pizza + cost of the soda
E = 4P + 4S

Now, if you want to rearrange this answer so that you've got S in terms of E and P, you need to start by getting the term containing S on one side of the equals sign by itself. Subtract 4P from both sides of the equation:

E - 4P = 4P + 4S - 4P
E - 4P = 4S

But you want 1S, or just S....do you see that the right side is 4 times as big as it should be? To get 1S, or just S, you can divide both sides of the equation by 4.
 
From [1]: 1 slice of pizza = $4, 1 can of soda = $4 ....expensive calories!
From [2]: Dave spends a total of $E
From [3]: pizza slices purchased = P, cans of soda purchases = S

SO quite evident: e) E = 4P + 4S

4S = E - 4P
S = E/4 - 4P/4
S = E/4 - P

That's pretty basic stuff Silver; make sure you understand it.

But if 1 pizza and 1 soda is $4, wouldn't 4P and 4S be $16 respectively?
 
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