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Carla's credit card statement showed a balance that was 0.72 dollars greater than what she had recorded. She realized she had made a payment of p . q r dollars and recorded it as p . r q dollars, where p, q, and r represent digits from 0 through 9. Which of the following could be the value of r?

Explanation	Calculations	Help
$We translate the difference between what was recorded and the actual payment into an equation.$	$(p . r q) - (p . q r) = 0.72$
$We express each decimal amount in terms of p, q, and r using place value.$	$(p + \frac{r}{10} + \frac{q}{100}) - (p + \frac{q}{10} + \frac{r}{100}) = 0.72$	Theory & Tactics Method Card TRANS5-G Click to view full details
$We combine like terms and simplify the difference.$	$\frac{r}{10} + \frac{q}{100} - \frac{q}{10} - \frac{r}{100} = 0.72 \frac{10 r + q - 10 q - r}{100} = 0.72 \frac{9 ( r - q )}{100} = 0.72$
$We remove the fraction by multiplying both sides by 100 and then isolate r - q.$	$9 (r - q) = 72 r - q = 8$
$We determine the digit values consistent with r - q = 8.$	$r = q + 8 possible q values are 0 or 1 possible r values are 8 or 9$

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C

Carla's credit card statement showed a balance that was 0.72 dollars greater than what she had recorded. She realized she had made a payment of p . q r dollars and recorded it as p . r q dollars, where p, q, and r represent digits from 0 through 9. Which of the following could be the value of r?

Explanation	Calculations	Help
$We translate the difference between what was recorded and the actual payment into an equation.$	$(p . r q) - (p . q r) = 0.72$
$We express each decimal amount in terms of p, q, and r using place value.$	$(p + \frac{r}{10} + \frac{q}{100}) - (p + \frac{q}{10} + \frac{r}{100}) = 0.72$	Theory & Tactics Method Card TRANS5-G Click to view full details
$We combine like terms and simplify the difference.$	$\frac{r}{10} + \frac{q}{100} - \frac{q}{10} - \frac{r}{100} = 0.72 \frac{10 r + q - 10 q - r}{100} = 0.72 \frac{9 ( r - q )}{100} = 0.72$
$We remove the fraction by multiplying both sides by 100 and then isolate r - q.$	$9 (r - q) = 72 r - q = 8$
$We determine the digit values consistent with r - q = 8.$	$r = q + 8 possible q values are 0 or 1 possible r values are 8 or 9$

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C