SOLUTION: Hi 2 cups 2 saucers and a teapot cost $30.20 A cup costs twice as much as a saucer. The teapot cost $7 more than a saucer. What is the cost of the teapot. Thanks. My son found

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Question 1204692: Hi
2 cups 2 saucers and a teapot cost $30.20 A cup costs twice as much as a saucer. The teapot cost $7 more than a saucer. What is the cost of the teapot. Thanks.
My son found a solution with fractions. Could I have a second opinion please
Found 4 solutions by josgarithmetic, math_tutor2020, greenestamps, ikleyn:
Answer by josgarithmetic(39629)   (Show Source): You can put this solution on YOUR website!
ITEM        PRICE          QTY.       COST
Cup          2x             2
Saucer        x             2
Teapot       x+7            1
TOTAL                                 30.20

Notice in the description the cup and the teapot prices are described in relation to a saucer. 

ITEM        PRICE          QTY.       COST
Cup          2x             2        2x*2=4x
Saucer        x             2          2x
Teapot       x+7            1         x+7
TOTAL                                 30.20


.
.
x, for saucer price to the nearest 1 cent, $3.31.
.The teapot price is $10.31
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

x = cost of one saucer
x+7 = cost of one teapot
2x = cost of one cup

2x = cost of 2 saucers
2*2x = 4x = cost of 2 cups

(4x)+(2x)+(x+7) = cost of 2 cups, 2 saucers, and 1 teapot
(4x)+(2x)+(x+7) = 30.20

Let's solve for x
(4x)+(2x)+(x+7) = 30.20
4x+2x+x+7 = 30.20
7x+7 = 30.20
7x = 30.20-7
7x = 23.20
x = 23.20/7
x = 3.3142857 approximately
x = 3.31 is the cost of one saucer when rounding to the nearest cent
x+7 = 3.31 + 7 = 10.31 is the cost of one teapot
2x = 2*3.31 = 6.62 is the cost of one cup


Check:
2 cups + 2 saucers + 1 teapot = 2*6.62 + 2*3.31 + 10.31 = 30.17
which is somewhat close to the goal of 30.20
Things are off a bit because we went from 3.3142857 to 3.31

There might be a typo with one or more of the numbers given by the teacher.
I recommend contacting your son's teacher for clarification.
Answer by greenestamps(13208)   (Show Source): You can put this solution on YOUR website!


As shown by the other tutors, the given numbers yield a solution which is not in whole numbers, so the numbers are not right.

So your son's answer with fractions was probably right.

Check the problem as it was given to see if you are using the right numbers; if so, let the teacher know the numbers in the problem are wrong.
Answer by ikleyn(52873)   (Show Source): You can put this solution on YOUR website!
.

For this problem, we look for a solution, which is integer number of cents.

In this problem, the solution CAN NOT be an arbitrary real number, if it is not an integer number of cents.


            Agree ?


The given problem has no answer for the price in integer number of cents.

So, the problem as posed in the post is  DEFECTIVE:  it has no a proper solution, at all.


Yes, the formal solution to equations could be obtained and expressed using fractions.

But at the end a person who solves the problem, must check if the fraction represents
an integer number of cents.

If not  (as in this case),  then the formal solution of equations in fractions
is not a solution to the problem.


Is everything clear to you from my explanation ?


--------------------


In such conditions, it is the student’s a voluntary duty to report to the teacher about the defect found,
and it is the teacher’s duty to inform the author of a textbook and/or the publishing company about this fact.


Usually, the authors are very happy to get a feedback from readers/students,
and are very grateful for noticing their mistakes.



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