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Alice's bank statement showed a balance that was 0.81 g re a t er t han w ha t h erc h ec kb oo k s h o w e d . S h e d i sco v ere d t ha t s h e ha d w r i tt e na c h ec k f or c.de d o ll a rs an d ha d recor d e d i t a s c.ed d o ll a rs, w h eree a c h o f c, d, an d e re p rese n t s a d i g i t f ro m 0 t h ro ug h 9. Whi c h o f t h e f o ll o w in g co u l d b e t h e v a l u eo f e$?

Explanation	Calculations	Help
$We set up an equation for the difference between the recorded check amount "c.ed dollars" and the actual check amount "c.de dollars" .$	$c . e d - c . d e = 0.81$
$We translate each decimal into its digit form using place values.$	$(c + \frac{e}{10} + \frac{d}{100}) - (c + \frac{d}{10} + \frac{e}{100}) = 0.81$	Theory & Tactics Method Card TRANS5-G Click to view full details
$We combine like terms into a single fraction.$	$\frac{9e - 9d}{100} = 0.81$$
$We clear the denominator by multiplying both sides by 100 and simplify.$	$9 e - 9 d = 0.81 \times 100" 9e - 9d = 81" e - d = 9$
$Since e and d are digits from 0 to 9 and their difference is 9, the only possibility is that e = 9 and d = 0, so e is 9.$	$e - d = 9" Only possible digits are e = 9 and d = 0" So e = 9$

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D

Alice's bank statement showed a balance that was 0.81 g re a t er t han w ha t h erc h ec kb oo k s h o w e d . S h e d i sco v ere d t ha t s h e ha d w r i tt e na c h ec k f or c.de d o ll a rs an d ha d recor d e d i t a s c.ed d o ll a rs, w h eree a c h o f c, d, an d e re p rese n t s a d i g i t f ro m 0 t h ro ug h 9. Whi c h o f t h e f o ll o w in g co u l d b e t h e v a l u eo f e$?

Explanation	Calculations	Help
$We set up an equation for the difference between the recorded check amount "c.ed dollars" and the actual check amount "c.de dollars" .$	$c . e d - c . d e = 0.81$
$We translate each decimal into its digit form using place values.$	$(c + \frac{e}{10} + \frac{d}{100}) - (c + \frac{d}{10} + \frac{e}{100}) = 0.81$	Theory & Tactics Method Card TRANS5-G Click to view full details
$We combine like terms into a single fraction.$	$\frac{9e - 9d}{100} = 0.81$$
$We clear the denominator by multiplying both sides by 100 and simplify.$	$9 e - 9 d = 0.81 \times 100" 9e - 9d = 81" e - d = 9$
$Since e and d are digits from 0 to 9 and their difference is 9, the only possibility is that e = 9 and d = 0, so e is 9.$	$e - d = 9" Only possible digits are e = 9 and d = 0" So e = 9$

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D