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Each of the 25 researchers at Lab Z will receive a grant this year. Phaedra’s grant is the largest, but it is only 300 dollars more than Quinn’s grant, and no grant is smaller than Quinn’s. If the total amount allocated for the grants is 60, 000 dollars, what is the amount of the largest grant Phaedra can receive?

Explanation	Calculations	Help
$We create variables for the grants for Phaedra and Quinn.$	$P = grant for Phaedra Q = grant for Quinn$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate "only 300 dollars more than Quinn's grant" into an equation.$	$P = Q + 300$	Theory & Tactics Method Card TRANS1-C Click to view full details
$We interpret "no grant is smaller than Quinn's grant", so to maximize Phaedra's grant, we assign each of the other 23 grants equal to Q .$	$Each of the other 23 grants = Q$	Theory & Tactics Method Card TRANS4-B Click to view full details
$We translate "the total amount allocated for the grants is 60,000 dollars" into an equation.$	$P + Q + 23 Q = 60000$	Theory & Tactics Method Card TRANS1-B Click to view full details
$We substitute P = Q + 300 into the total and simplify to isolate Q .$	$(Q + 300) + 24 Q = 60000 25 Q + 300 = 60000$	Theory & Tactics Method Card EQUA1-B Click to view full details
$We subtract 300 from both sides and divide by 25 to find Q .$	$25 Q = 60000 - 300 = 59700 Q = \frac{59700}{25} = 2388$	Theory & Tactics Method Card EQUA1-C Click to view full details
$We add 300 to Quinn's grant to find Phaedra's grant.$	$P = 2388 + 300 = 2688$

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D

Each of the 25 researchers at Lab Z will receive a grant this year. Phaedra’s grant is the largest, but it is only 300 dollars more than Quinn’s grant, and no grant is smaller than Quinn’s. If the total amount allocated for the grants is 60, 000 dollars, what is the amount of the largest grant Phaedra can receive?

Explanation	Calculations	Help
$We create variables for the grants for Phaedra and Quinn.$	$P = grant for Phaedra Q = grant for Quinn$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate "only 300 dollars more than Quinn's grant" into an equation.$	$P = Q + 300$	Theory & Tactics Method Card TRANS1-C Click to view full details
$We interpret "no grant is smaller than Quinn's grant", so to maximize Phaedra's grant, we assign each of the other 23 grants equal to Q .$	$Each of the other 23 grants = Q$	Theory & Tactics Method Card TRANS4-B Click to view full details
$We translate "the total amount allocated for the grants is 60,000 dollars" into an equation.$	$P + Q + 23 Q = 60000$	Theory & Tactics Method Card TRANS1-B Click to view full details
$We substitute P = Q + 300 into the total and simplify to isolate Q .$	$(Q + 300) + 24 Q = 60000 25 Q + 300 = 60000$	Theory & Tactics Method Card EQUA1-B Click to view full details
$We subtract 300 from both sides and divide by 25 to find Q .$	$25 Q = 60000 - 300 = 59700 Q = \frac{59700}{25} = 2388$	Theory & Tactics Method Card EQUA1-C Click to view full details
$We add 300 to Quinn's grant to find Phaedra's grant.$	$P = 2388 + 300 = 2688$

Scroll horizontally to view all columns

D