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Each of the 22 contestants in a talent competition is awarded some number of points. Olivia earns the fewest points, and Nancy earns the most points; Nancy’s score exceeds Olivia’s by exactly 400 points. If the total number of points awarded is 40000, what is the greatest number of points Nancy can receive?

Explanation	Calculations	Help
$We name the score for Nancy as N and the score for Olivia as O .$	$N = Nancy’s score O = Olivia’s score$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate "Nancy's score exceeds Olivia's by exactly 400 points" into an equation for their score difference.$	$N = O + 400$	Theory & Tactics Method Card TRANS1-C Click to view full details
$To maximize Nancy's score, we give each of the other 20 contestants the same score as Olivia. We translate "the total number of points awarded is 40000" into an equation summing Nancy's score and all 21 copies of Olivia's score.$	$N + 21 O = 40000$	Theory & Tactics Method Card TRANS1-C Click to view full details
$We substitute N = O + 400 into the total equation.$	$(O + 400) + 21 O = 40000$	Theory & Tactics Method Card EQUA1-B Click to view full details
$We subtract 400 from both sides and then divide by 22 to isolate O .$	$22 O = 40000 - 400 = 39600 O = \frac{39600}{22} = 1800$	Theory & Tactics Method Card EQUA1-C Click to view full details
$We add 400 to Olivia's score to find Nancy's score.$	$N = 1800 + 400 = 2200$

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B

Each of the 22 contestants in a talent competition is awarded some number of points. Olivia earns the fewest points, and Nancy earns the most points; Nancy’s score exceeds Olivia’s by exactly 400 points. If the total number of points awarded is 40000, what is the greatest number of points Nancy can receive?

Explanation	Calculations	Help
$We name the score for Nancy as N and the score for Olivia as O .$	$N = Nancy’s score O = Olivia’s score$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate "Nancy's score exceeds Olivia's by exactly 400 points" into an equation for their score difference.$	$N = O + 400$	Theory & Tactics Method Card TRANS1-C Click to view full details
$To maximize Nancy's score, we give each of the other 20 contestants the same score as Olivia. We translate "the total number of points awarded is 40000" into an equation summing Nancy's score and all 21 copies of Olivia's score.$	$N + 21 O = 40000$	Theory & Tactics Method Card TRANS1-C Click to view full details
$We substitute N = O + 400 into the total equation.$	$(O + 400) + 21 O = 40000$	Theory & Tactics Method Card EQUA1-B Click to view full details
$We subtract 400 from both sides and then divide by 22 to isolate O .$	$22 O = 40000 - 400 = 39600 O = \frac{39600}{22} = 1800$	Theory & Tactics Method Card EQUA1-C Click to view full details
$We add 400 to Olivia's score to find Nancy's score.$	$N = 1800 + 400 = 2200$

Scroll horizontally to view all columns

B