Jorge's bank statement showed a balance that was 0.54 dollars greater than what his records...

Question

Jorge's bank statement showed a balance that was 0.54 dollars greater than what his records showed. He discovered that he had written a check for x.yz dollars and had recorded it as x.zy dollars, where each of x, y, and z represents a digit from 0 though 9. Which of the following could be the value of z ?

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6 We translate the phrases to set up the difference between the recorded and actual check amounts. "recorded it as x.zy dollars" - "written a check for x.yz dollars" = 0.54 We write each amount in terms of x, y, and z based on place value. x + z/10 + y/100 - (x + y/10 + z/100) = 0.54 We combine like terms to simplify the expression. 9(z - y)/100 = 0.54 We clear the denominator and solve for the difference. 9(z - y) = 0.54 100 9(z - y) = 54 z - y = 6 Since z and y are digits from 0 to 9 and their difference is 6, z could be 6, 7, 8, or 9, and among the answer choices only 6 appears. z - y = 6 Possible values for z are 6, 7, 8, or 9 Only 6 appears in the answer choices

Explanation	Calculations	Help
$We translate the phrases to set up the difference between the recorded and actual check amounts.$	$"recorded it as x.zy dollars " - " written a check for x.yz dollars" = 0.54$
$We write each amount in terms of x, y, and z based on place value.$	$x + \frac{z}{10} + \frac{y}{100} - (x + \frac{y}{10} + \frac{z}{100}) = 0.54$
$We combine like terms to simplify the expression.$	$\frac{9 ( z - y )}{100} = 0.54$
$We clear the denominator and solve for the difference.$	$9 (z - y) = 0.54 \times 100 9 (z - y) = 54 z - y = 6$
$Since z and y are digits from 0 to 9 and their difference is 6, z could be 6, 7, 8, or 9, and among the answer choices only 6 appears.$	$z - y = 6 Possible values for z are 6, 7, 8, or 9 Only 6 appears in the answer choices$

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