Please explain how to solve this problem.
A bank teller accidentally switches the dollars and cents when he cashed a check for Mr. Jones, giving him dollars instead of cents, and cents instead of dollars, After buying a five cent candy, Mr. Jones discovered he now has exactly twce as much money as his original check. What was the amount of the check?
Thank you! I appreciate the help!
A bank teller accidentally switches the dollars and cents when he cashed a check for Mr. Jones, giving him dollars instead of cents, and cents instead of dollars, After buying a five cent candy, Mr. Jones discovered he now has exactly twce as much money as his original check. What was the amount of the check?
Thank you! I appreciate the help!
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Let d be the dollar amount of the check and
c be the cents amount of the check
The value of the check, v = d + c/100
The money provided by the teller to Mr. Jones, t = c + d/100
t - 0.05 = 2v { After buying a five cent candy, Mr. Jones discovered he now has exactly twice as much money as his original check. }
Substituting for t and v:
(c + d/100) - 0.05 = 2(d + c/100)
(100c + d) - 5 = 2(100d + c)
100c + d - 5 = 200d + 2c
98c - 5 = 199d
c and d must both be non-negative integers and 0 <= c <= 99.
I know there is something you can exploit to make it easy to find the final solution, but I can't remember what it is. By trial and error (a spreadsheet made it easy) I found c = 63 and d = 31. The check was for $31.63.
c be the cents amount of the check
The value of the check, v = d + c/100
The money provided by the teller to Mr. Jones, t = c + d/100
t - 0.05 = 2v { After buying a five cent candy, Mr. Jones discovered he now has exactly twice as much money as his original check. }
Substituting for t and v:
(c + d/100) - 0.05 = 2(d + c/100)
(100c + d) - 5 = 2(100d + c)
100c + d - 5 = 200d + 2c
98c - 5 = 199d
c and d must both be non-negative integers and 0 <= c <= 99.
I know there is something you can exploit to make it easy to find the final solution, but I can't remember what it is. By trial and error (a spreadsheet made it easy) I found c = 63 and d = 31. The check was for $31.63.
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$5.20