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Each of the 20 employees at Company J is to receive an end-of-year bonus this year. Agnes will receive a larger bonus than any other employee, but only 500USD more than Cheryl will receive. None of the employees will receive a smaller bonus than Cheryl. If the amount of money to be distributed in bonuses at Company J this year totals 60,000USD, what is the largest bonus Agnes can receive?

Explanation	Calculations	Help
$We name the bonus for Agnes as A and the bonus for Cheryl as C.$	$A = bonus for Agnes C = bonus for Cheryl$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate "only 500USD more than Cheryl will receive" into an equation.$	$A = C + 500$	Theory & Tactics Method Card TRANS1-C Click to view full details
$We interpret "None of the employees will receive a smaller bonus than Cheryl", so to make Agnes's bonus as large as possible, we assign each of the other 18 employees exactly C.$	$Each of the other 18 bonuses = C$	Theory & Tactics Method Card TRANS4-B Click to view full details
$We translate "totals 60,000USD" into an equation for all bonuses.$	$A + C + 18 C = 60000$	Theory & Tactics Method Card TRANS1-C Click to view full details
$We substitute the expression for A into the total and simplify to isolate C.$	$(C + 500) + 19 C = 60000 20 C + 500 = 60000$	Theory & Tactics Method Card EQUA3-A Click to view full details Theory & Tactics Method Card EQUA1-B Click to view full details
$We subtract 500 from both sides and divide by 20 to find C.$	$20 C = 60000 - 500 = 59500 C = \frac{59500}{20} = 2975$	Theory & Tactics Method Card EQUA1-C Click to view full details
$We add 500 to Cheryl's bonus to find Agnes's bonus.$	$A = 2975 + 500 = 3475$

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3475 USD

Each of the 20 employees at Company J is to receive an end-of-year bonus this year. Agnes will receive a larger bonus than any other employee, but only 500USD more than Cheryl will receive. None of the employees will receive a smaller bonus than Cheryl. If the amount of money to be distributed in bonuses at Company J this year totals 60,000USD, what is the largest bonus Agnes can receive?

Explanation	Calculations	Help
$We name the bonus for Agnes as A and the bonus for Cheryl as C.$	$A = bonus for Agnes C = bonus for Cheryl$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate "only 500USD more than Cheryl will receive" into an equation.$	$A = C + 500$	Theory & Tactics Method Card TRANS1-C Click to view full details
$We interpret "None of the employees will receive a smaller bonus than Cheryl", so to make Agnes's bonus as large as possible, we assign each of the other 18 employees exactly C.$	$Each of the other 18 bonuses = C$	Theory & Tactics Method Card TRANS4-B Click to view full details
$We translate "totals 60,000USD" into an equation for all bonuses.$	$A + C + 18 C = 60000$	Theory & Tactics Method Card TRANS1-C Click to view full details
$We substitute the expression for A into the total and simplify to isolate C.$	$(C + 500) + 19 C = 60000 20 C + 500 = 60000$	Theory & Tactics Method Card EQUA3-A Click to view full details Theory & Tactics Method Card EQUA1-B Click to view full details
$We subtract 500 from both sides and divide by 20 to find C.$	$20 C = 60000 - 500 = 59500 C = \frac{59500}{20} = 2975$	Theory & Tactics Method Card EQUA1-C Click to view full details
$We add 500 to Cheryl's bonus to find Agnes's bonus.$	$A = 2975 + 500 = 3475$

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3475 USD