SOLUTION: Javonne purchased some art supplies and paid for them with a $20 bill. The cashier handed her c dollars in change, which was a mistake. To ﬁx the mistake, Javonne returned $1.

Question 1195141: Javonne purchased some art supplies and paid for
them with a $20 bill. The cashier handed her c
dollars in change, which was a mistake. To ﬁx the
mistake, Javonne returned $1.00 to the cashier. lf
she purchase price was twice the amount of change
that Javonne was originally given, what is the value
of c?
Found 3 solutions by Theo, greenestamps, ikleyn:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
i get the following.
p = purchase price.
c = original change
c-1 = correct change
since p = 2 * the original change, then p = 2c
20 dollars was used to pay for the purchase price.
20 minus the purchase price equals the change.
therefore:
c = 20 - p
since p = 2c, you get:
c = 20 - 2c
solve for c to get:
c = 20/3
that's the original change.
the corrected change is c - 1 = 20/3 - 3/3 = 17/3.
you were asked what the value of c was.
that's the original change.
your solution is that the original change = c = 20/3 = 6.67 rounded to the nearest penny.
to confirm 6.67 as the original change equal to c, i did the following:
the purchase price was 14.33.
the original change was 6.67
20 - 6.67 = 13.3
that's 1 dollar short of the purchase price.
to correct, 1 dollar was given back.
that made the purchase price equal to 20 - 5.67 = 14.33, correcting the mistake.
let me know if you have any questions.
theo
Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!

Somewhere in his analysis the other tutor made a mistake....

The purchase price was p; the amount of change Javonne originally received was c.

Since the situation was corrected by returning $1 to the cashier, the correct change was c-1.

The purchase price was twice the original amount of change, so p=2c.

The purchase price, plus the corrected amount of change, was $20:

The purchase price was 2c = $14.
The original amount of change was c = $7.
The correct amount of change was c-1 = $6.
The purchase price plus the correct amount of change was $14 + $6 = $20.

ANSWER: c, the original amount of change, was $7

Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.
Javonne purchased some art supplies and paid for them with a $20 bill.
The cashier handed her c dollars in change, which was a mistake.
To ﬁx the mistake, Javonne returned $1.00 to the cashier.
lf she purchase price was twice the amount of change
that Javonne was originally given, what is the value of c?
~~~~~~~~~~~~~~~~~~~~~~

From the condition, the price of the purchase was 20-c+1 dollars. It is given that this price is twice as the amount of "c", so we write an equation 20 - c + 1 = 2c. It can be solved in couple of lines 20 + 1 = 2c + c 21 = 3c c = 21/3 = 7. ANSWER. The value of "c" is 7 dollars.

Solved.

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

This problem is good (and such problems are good), when a teacher wants to train a young pupils
to setup and to solve non-standard problems.

At such circumstances, than simpler a solution approach is, than it is better.

It is why I came with this solution.

With it, using one single equation for setup, the solution can be explained
to a 5-th grade student, who just started to learn problems with one equation,
but did not learn systems of equations, yet.

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