Morgan and Riley are ordering hats and scarves for... | Free GMAT Practice Question | GMAT Panda

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Morgan and Riley are ordering hats and scarves for a fundraiser. Morgan thinks that the number of hats should be twice the number of scarves (H = 2 S), but Riley thinks the number of scarves should be 6 more than one-third of the number of hats (S = \frac{1}{3} H + 6). How many hats should they order so that Morgan and Riley agree on the number of scarves to order?

Explanation	Calculations	Help
$We first create variables to represent the number of hats and scarves.$	$H = number of hats S = number of scarves$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate Morgan's statement "the number of hats should be twice the number of scarves" into an equation.$	$H = 2 S$	Theory & Tactics Method Card TRANS1-E Click to view full details
$We translate Riley's statement "the number of scarves should be 6 more than one-third of the number of hats" into an equation.$	$S = \frac{1}{3} H + 6$	Theory & Tactics Method Card TRANS2-B Click to view full details Theory & Tactics Method Card TRANS1-C Click to view full details
$We substitute the expression for H from Morgan's equation into Riley's equation.$	$S = \frac{1}{3} (2 S) + 6$
$We subtract \frac{2}{3} S from both sides to group like terms.$	$S - \frac{2}{3} S = 6$	Theory & Tactics Method Card EQUA1-B Click to view full details
$We divide both sides by \frac{1}{3} to solve for S .$	$\frac{1}{3} S = 6 S = \frac{6}{\frac{1}{3}} = 6 \times 3 = 18$	Theory & Tactics Method Card EQUA1-C Click to view full details
$We substitute S = 18 into the equation H = 2 S to find H .$	$H = 2 \times 18 = 36$

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C

Morgan and Riley are ordering hats and scarves for a fundraiser. Morgan thinks that the number of hats should be twice the number of scarves (H = 2 S), but Riley thinks the number of scarves should be 6 more than one-third of the number of hats (S = \frac{1}{3} H + 6). How many hats should they order so that Morgan and Riley agree on the number of scarves to order?

Explanation	Calculations	Help
$We first create variables to represent the number of hats and scarves.$	$H = number of hats S = number of scarves$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate Morgan's statement "the number of hats should be twice the number of scarves" into an equation.$	$H = 2 S$	Theory & Tactics Method Card TRANS1-E Click to view full details
$We translate Riley's statement "the number of scarves should be 6 more than one-third of the number of hats" into an equation.$	$S = \frac{1}{3} H + 6$	Theory & Tactics Method Card TRANS2-B Click to view full details Theory & Tactics Method Card TRANS1-C Click to view full details
$We substitute the expression for H from Morgan's equation into Riley's equation.$	$S = \frac{1}{3} (2 S) + 6$
$We subtract \frac{2}{3} S from both sides to group like terms.$	$S - \frac{2}{3} S = 6$	Theory & Tactics Method Card EQUA1-B Click to view full details
$We divide both sides by \frac{1}{3} to solve for S .$	$\frac{1}{3} S = 6 S = \frac{6}{\frac{1}{3}} = 6 \times 3 = 18$	Theory & Tactics Method Card EQUA1-C Click to view full details
$We substitute S = 18 into the equation H = 2 S to find H .$	$H = 2 \times 18 = 36$

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C