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A bowl contains 105 marbles, all of which are red, green, or blue. If the bowl contains m red marbles and 7 more green marbles than red, which of the following gives the number of blue marbles the bowl contains in terms of m ?

Explanation	Calculations	Help
$We first create non-ambiguous variables for each color of marble.$	$m = number of red marbles g = number of green marbles b = number of blue marbles$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate the relative comparison "7 more green marbles than red" into a mathematical expression.$	$g = m + 7$	Theory & Tactics Method Card TRANS1-C Click to view full details
$We translate the total count statement "A bowl contains 105 marbles" into an equation for the sum of the marbles.$	$m + g + b = 105$	Theory & Tactics Method Card TRANS1-B Click to view full details Theory & Tactics Method Card TRANS1-C Click to view full details
$We substitute the expression for g into the total and isolate b .$	$m + (m + 7) + b = 105 2 m + 7 + b = 105 2 m + b = 98 b = 98 - 2 m$	Theory & Tactics Method Card EQUA1-A Click to view full details

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C

A bowl contains 105 marbles, all of which are red, green, or blue. If the bowl contains m red marbles and 7 more green marbles than red, which of the following gives the number of blue marbles the bowl contains in terms of m ?

Explanation	Calculations	Help
$We first create non-ambiguous variables for each color of marble.$	$m = number of red marbles g = number of green marbles b = number of blue marbles$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate the relative comparison "7 more green marbles than red" into a mathematical expression.$	$g = m + 7$	Theory & Tactics Method Card TRANS1-C Click to view full details
$We translate the total count statement "A bowl contains 105 marbles" into an equation for the sum of the marbles.$	$m + g + b = 105$	Theory & Tactics Method Card TRANS1-B Click to view full details Theory & Tactics Method Card TRANS1-C Click to view full details
$We substitute the expression for g into the total and isolate b .$	$m + (m + 7) + b = 105 2 m + 7 + b = 105 2 m + b = 98 b = 98 - 2 m$	Theory & Tactics Method Card EQUA1-A Click to view full details

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C