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Each of the 16 consultants at Consulting Group Q is to receive a profit-sharing distribution this year. Carmen will receive a distribution larger than any other consultant, but only 800 dollars more than Devon will receive. None of the consultants will receive a distribution smaller than Devon. If the total amount to be distributed is 80, 800 dollars, what is the largest distribution Carmen can receive?

Explanation	Calculations	Help
$We name the distribution for Carmen as C and the distribution for Devon as D .$	$C = distribution for Carmen D = distribution for Devon$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate "only 800 dollars more than Devon will receive" into an equation.$	$C = D + 800$	Theory & Tactics Method Card TRANS1-C Click to view full details
$We interpret "None of the consultants will receive a distribution smaller than Devon", so to maximize Carmen's distribution, we assign each of the other 14 distributions exactly D .$	$each of the other 14 distributions = D$	Theory & Tactics Method Card TRANS4-B Click to view full details
$We translate "the total amount to be distributed is 80,800 dollars" into an equation for all distributions.$	$C + D + 14 D = 80800$	Theory & Tactics Method Card TRANS1-B Click to view full details
$We substitute the expression for C into the total and simplify to isolate D .$	$(D + 800) + 15 D = 80800 16 D + 800 = 80800$	Theory & Tactics Method Card EQUA1-B Click to view full details
$We subtract 800 from both sides and divide by 16 to find D .$	$16 D = 80800 - 800 = 80000 D = \frac{80000}{16} = 5000$	Theory & Tactics Method Card EQUA1-C Click to view full details
$We add 800 to Devon's distribution to find Carmen's distribution.$	$C = 5000 + 800 = 5800$

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B

Each of the 16 consultants at Consulting Group Q is to receive a profit-sharing distribution this year. Carmen will receive a distribution larger than any other consultant, but only 800 dollars more than Devon will receive. None of the consultants will receive a distribution smaller than Devon. If the total amount to be distributed is 80, 800 dollars, what is the largest distribution Carmen can receive?

Explanation	Calculations	Help
$We name the distribution for Carmen as C and the distribution for Devon as D .$	$C = distribution for Carmen D = distribution for Devon$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate "only 800 dollars more than Devon will receive" into an equation.$	$C = D + 800$	Theory & Tactics Method Card TRANS1-C Click to view full details
$We interpret "None of the consultants will receive a distribution smaller than Devon", so to maximize Carmen's distribution, we assign each of the other 14 distributions exactly D .$	$each of the other 14 distributions = D$	Theory & Tactics Method Card TRANS4-B Click to view full details
$We translate "the total amount to be distributed is 80,800 dollars" into an equation for all distributions.$	$C + D + 14 D = 80800$	Theory & Tactics Method Card TRANS1-B Click to view full details
$We substitute the expression for C into the total and simplify to isolate D .$	$(D + 800) + 15 D = 80800 16 D + 800 = 80800$	Theory & Tactics Method Card EQUA1-B Click to view full details
$We subtract 800 from both sides and divide by 16 to find D .$	$16 D = 80800 - 800 = 80000 D = \frac{80000}{16} = 5000$	Theory & Tactics Method Card EQUA1-C Click to view full details
$We add 800 to Devon's distribution to find Carmen's distribution.$	$C = 5000 + 800 = 5800$

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B