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A jar contains 84 marbles, each of which is blue, green, or red. If the jar contains g green marbles and there are 3 more blue marbles than twice the number of green marbles, which of the following gives the number of red marbles in terms of g ?

Explanation	Calculations	Help
$We first create non-ambiguous variables for each color of marble.$	$g = number of green marbles b = number of blue marbles r = number of red marbles$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate the relative comparison "there are 3 more blue marbles than twice the number of green marbles" into a mathematical expression.$	$b = 2 g + 3$	Theory & Tactics Method Card TRANS1-C Click to view full details
$We translate the total count statement "A jar contains 84 marbles" into an equation for the sum of the marbles.$	$g + b + r = 84$	Theory & Tactics Method Card TRANS1-B Click to view full details Theory & Tactics Method Card TRANS1-C Click to view full details
$We substitute the expression for b into the total and then isolate r .$	$g + (2 g + 3) + r = 84 3 g + 3 + r = 84 3 g + r = 81 r = 81 - 3 g$	Theory & Tactics Method Card EQUA1-A Click to view full details

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C

A jar contains 84 marbles, each of which is blue, green, or red. If the jar contains g green marbles and there are 3 more blue marbles than twice the number of green marbles, which of the following gives the number of red marbles in terms of g ?

Explanation	Calculations	Help
$We first create non-ambiguous variables for each color of marble.$	$g = number of green marbles b = number of blue marbles r = number of red marbles$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate the relative comparison "there are 3 more blue marbles than twice the number of green marbles" into a mathematical expression.$	$b = 2 g + 3$	Theory & Tactics Method Card TRANS1-C Click to view full details
$We translate the total count statement "A jar contains 84 marbles" into an equation for the sum of the marbles.$	$g + b + r = 84$	Theory & Tactics Method Card TRANS1-B Click to view full details Theory & Tactics Method Card TRANS1-C Click to view full details
$We substitute the expression for b into the total and then isolate r .$	$g + (2 g + 3) + r = 84 3 g + 3 + r = 84 3 g + r = 81 r = 81 - 3 g$	Theory & Tactics Method Card EQUA1-A Click to view full details

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C