David and Ron are ordering food for a business lun... | Free GMAT Practice Question | GMAT Panda

👋 Hi! I'm GMAT Panda. Ask me anything about this question, or click a button below to get started!

David and Ron are ordering food for a business lunch. David thinks that there should be twice as many sandwiches as there are pastries, but Ron thinks the number of pastries should be 12 more than one-fourth of the number of sandwiches. How many sandwiches should be ordered so that David and Ron can agree on the number of pastries to order?

Explanation	Calculations	Help
$We first create variables to represent the number of sandwiches and pastries.$	$S = number of sandwiches P = number of pastries$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate David's statement "twice as many sandwiches as there are pastries" into an equation.$	$S = 2 P$	Theory & Tactics Method Card TRANS1-E Click to view full details
$We translate Ron's statement "number of pastries should be 12 more than one-fourth of the number of sandwiches" into an equation.$	$P = \frac{1}{4} S + 12$	Theory & Tactics Method Card TRANS2-B Click to view full details Theory & Tactics Method Card TRANS1-C Click to view full details
$We substitute the expression for S from David's equation into Ron's equation to write it in terms of P .$	$P = \frac{1}{4} (2 P) + 12$
$We subtract \frac{1}{2} P from both sides to group like terms.$	$P - \frac{1}{2} P = 12$	Theory & Tactics Method Card EQUA1-B Click to view full details
$We divide both sides by \frac{1}{2} to solve for P .$	$\frac{1}{2} P = 12 P = \frac{12}{\frac{1}{2}} = 12 \times 2 = 24$	Theory & Tactics Method Card EQUA1-C Click to view full details
$We substitute P = 24 into the equation S = 2 P to find S .$	$S = 2 \times 24 = 48$

Scroll horizontally to view all columns

48 sandwiches

David and Ron are ordering food for a business lunch. David thinks that there should be twice as many sandwiches as there are pastries, but Ron thinks the number of pastries should be 12 more than one-fourth of the number of sandwiches. How many sandwiches should be ordered so that David and Ron can agree on the number of pastries to order?

Explanation	Calculations	Help
$We first create variables to represent the number of sandwiches and pastries.$	$S = number of sandwiches P = number of pastries$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate David's statement "twice as many sandwiches as there are pastries" into an equation.$	$S = 2 P$	Theory & Tactics Method Card TRANS1-E Click to view full details
$We translate Ron's statement "number of pastries should be 12 more than one-fourth of the number of sandwiches" into an equation.$	$P = \frac{1}{4} S + 12$	Theory & Tactics Method Card TRANS2-B Click to view full details Theory & Tactics Method Card TRANS1-C Click to view full details
$We substitute the expression for S from David's equation into Ron's equation to write it in terms of P .$	$P = \frac{1}{4} (2 P) + 12$
$We subtract \frac{1}{2} P from both sides to group like terms.$	$P - \frac{1}{2} P = 12$	Theory & Tactics Method Card EQUA1-B Click to view full details
$We divide both sides by \frac{1}{2} to solve for P .$	$\frac{1}{2} P = 12 P = \frac{12}{\frac{1}{2}} = 12 \times 2 = 24$	Theory & Tactics Method Card EQUA1-C Click to view full details
$We substitute P = 24 into the equation S = 2 P to find S .$	$S = 2 \times 24 = 48$

Scroll horizontally to view all columns

48 sandwiches