SOLUTION: A confused bank teller transposed the dollars and cents when he cashed a check for Ms. Smith, giving her dollars instead of cents and cents instead of dollars. After buying a newsp

Question 490608: A confused bank teller transposed the dollars and cents when he cashed a check for Ms. Smith, giving her dollars instead of cents and cents instead of dollars. After buying a newspaper for 50 cents, Ms. Smith noticed that she had left exactly three times as much as the original check. What was the amount of the check?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A confused bank teller transposed the dollars and cents when he cashed a check for Ms. Smith, giving her dollars instead of cents and cents instead of dollars.
After buying a newspaper for 50 cents, Ms. Smith noticed that she had left exactly three times as much as the original check.
What was the amount of the check?
:
Let x = correct no. of dollars
Let .01y = correct no. of cents (in dollars)
then
x + .01y = correct amt
y + .01x = the incorrect amt
:
y + .01x - .50 = 3(x + .01y)
y + .01x - .50 = 3x + .03y
y - .03y = 3x - .01x + .50
.97y = 2.99x + .50
get rid of those decimals, mult by 100
97y = 299x + 50
divide both sides by 97
y = x +
enter this equation into Ti83 or equiv and check the table of the graph
It will be apparent that he only integer solution of y occurs when
x = 18, y = 56, therefore
$18.56 is the correct amt
however the teller gave
$56.18
:
:
We can confirm this
56.18 - .50 = 3(18.56)
55.68 = 55.68
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