Elimination Method

[eddy2017]

mr.murphy is hosting a cookie decorating party to raise money for united way. ms, smith bought three plain cookies and decorated five cookies and she spent $21. mrs,thomas bought one plain cookie and decorated four cookies and she spent $14 . how much does a plain cookie cost ? how much does it cost to decorate a cookie ?

I have sweated over these type of problems right here before. Let me try this with all due respect to tutors here.
I would set this up like this:

Let x be the plain cookies

Let y be the decorated cookies and set up equations and then solve for x and y

Equation A 3x+ 5y= 21

Equation B 1x+ 4y = 14

Solving for y in equation B we get

x= 14-4y (equation C)

replacing x for its value , in equation A

3x+5y=21

3(14-4y) +5y =21

Distributing

42-12y+5y=21

Now solving for y

42-7y=21

Now solving for y

42 -7y-42= 21- 42

-7y= -21

-7y/-7 = -21/-7

y=3

Now we replace y for its value in equation C.

X= 14- 4Y

X= 14- 4(3)

X=14-12

X=2

How much does a regular cookie cost?

It costs 2 dollars.

How much does it cost to decorate a cookie?.

It costs 3 dollars.

 

[blamocur]

Looks good! The only potential issue is whether the cost of decorating a cookie is the same as the price of a decorated cookie? My interpretation is that the price of a decorated cookie is a sum of the price of an undecorated one and the cost of decorating it.

 

[eddy2017]

Thanks!.

 

[Steven G]

For the most part, it is good work.

I do however have a number of problems with your work.

1) You wrote Let x be the plain cookies. Well, is x the price of a plain cookie, how many plain cookies were purchased or something else?
2) You wrote Let y be the decorated cookies. Again, is y the price of a decorated cookie, how many decorated cookies were purchased, the price to decorate a cookie or something else?
3) You wrote Solving for y in equation B we get x= 14-4y (equation C). You did not solve for y, rather you solved for x.
4) You did not ask answer the question as pointed out by blamocur!!!!! You found out how much a decorated cookie cost. However you were asked how much it costs to decorate a cookie. That answer will be $3-$2 or $1.

 

[eddy2017]

Thanks!

 

[eddy2017]

For the most part, it is good work.

I do however have a number of problems with your work.

1) You wrote Let x be the plain cookies. Well, is x the price of a plain cookie, how many plain cookies were purchased or something else?
2) You wrote Let y be the decorated cookies. Again, is y the price of a decorated cookie, how many decorated cookies were purchased, the price to decorate a cookie or something else?
3) You wrote Solving for y in equation B we get x= 14-4y (equation C). You did not solve for y, rather you solved for x.
4) You did not ask answer the question as pointed out by blamocur!!!!! You found out how much a decorated cookie cost. However you were asked how much it costs to decorate a cookie. That answer will be $3-$2 or $1.

I understand what you say. we are calculating the price of decorating the cookie, not the sum of the cookie and the decoration, though.
But looking at the questions in the posted problem, it is asking how much the regular cookie is worth and how much the decoration is worth. If it had asked how much a decorated cookie was worth, then we would have to add the cost of the cookie to the decoration.

 

[Steven G]

So what do you think the prices are for
each plain cookie?
each decorated cookie?
decorating a cookie?

 

[eddy2017]

So what do you think the prices are for
each plain cookie?
each decorated cookie?
decorating a cookie?

Mr Jomo, interesting question.
plain cookie $2

decorated cookie $3

cost of decorating a cookie?.
I will add both costs and then i think 5 dollars will be the cost of putting a decoration on one of these cookies.

 

[Otis]

i think 5 dollars will be the cost of putting a decoration on one of these cookies.

That's not correct, Eddy. Your previous answer is correct. A plain cookie costs $2, and the additional cost to add decoration is $3.

(I've guessed that your unreferenced pronoun in the phrase 'these cookies' refers to the plain cookies.)

$5 is what a customer would pay to purchase one decorated cookie (cookie cost plus decorating cost). But, the exercise in post #1 does not ask for that combined cost. Again, your first answer is correct.

 

[Otis]

My interpretation is that the price of a decorated cookie is a sum of the price of an undecorated one and the cost of decorating it.

My interpretation is that the exercise does not ask for the price of a decorated cookie. It asks for the decorating cost and the cookie cost separately.