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define variables, write equations, solve

cathyv

New member
Joined
Sep 22, 2009
Messages
4
Food stand sells popcorn for $2.50 and pretzels for $2.00. Sells $336 worth of popcorn and pretzels. They sell twice as many bags of popcorn as pretzels. How many of each do they sell?

thank you!
 

tkhunny

Moderator
Staff member
Joined
Apr 12, 2005
Messages
9,708
You appear to have excellent instructions. Why not follow them?

Let's see what you get for your variable definitions.
 

cathyv

New member
Joined
Sep 22, 2009
Messages
4
p=pretzels
2p=popcorn

2p+5p=336
7p=336
p=48
2p=96

did I figure it out?
 

tkhunny

Moderator
Staff member
Joined
Apr 12, 2005
Messages
9,708
Let's see...did you check your answers against the problem statement? Does p = 48 work?

Clean and precise will help you gain confidence and consistency.

Here's an example. I would do it this way.

Definitions:

Z = Bags of Pretzels Sold
C = Bags of Popcorn Sold

What does it want?

"How many of each do they sell?" Okay, so we'll need Z and C before we think we are done.

Equation Translation:

"They sell twice as many bags of popcorn as pretzels."

1) C = 2Z

"popcorn for $2.50 and pretzels for $2.00. Sells $336 worth of popcorn and pretzels.

2) $2.50 * C + $2.00 * Z = $336

Solution:

It appears that eauation 1 is already solved for "C", so simply substitute for "C" in equation 2.

3) $2.50 * (2Z) + $2.00 * Z = $336

Simplify and solve for Z

4) $5.00 * Z + $2.00 * Z = $336 (Substitution)
5) $7.00 * Z = $336 (Distributive Property)
6) Z = $336 / $7.00 = 48

Substitute this value of Z into equation 1

7) C = 2(48) = 96

Checking:

From Equation 1: 96 = 2*48 ==> 96 = 96 -- Check
From Equation 2: $2.50 * (96) + $2.00 * (48) = $336 ==> $240.00 + $96 = $336 ==> $336 = $336 -- Check

Answer:

C = 96 and Z = 48, so there were sold 48 bags of pretzels and 96 bags of popcorn.

See, you managed the same answer, but:
1) How easy is it to follow yours? Will it be obvious to a casual observer? Will it be obvious to you -- tomorrow?
2) Don't be afraid of defining multiple variables.
3) You provided no checking at all.
4) Rather than asking if it was correct, I took the time to prove that it was correct. This is the source of confidence.

Note: What I have demonstrated is great for writing textbooks and for leasurely exams. Also, this would be superb for someone grading your papers. However, if you have an exam under time pressure, you must move faster - much faster! This is why you must get fluent at clear, concise, and secure. You can add speed as you gain experience. Without the background I suggest, more speed will just poduce less confidence.
 
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