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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(13215)  (Show Source):
Answer by ikleyn(52903)  (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.
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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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